Math 10.9 edited makeMultQ, C#

Math 10.9 edited makeMultQ

//Rextester.Program.Main is the entry point for your code. Don't change it.
//Compiler version 4.0.30319.17929 for Microsoft (R) .NET Framework 4.5

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;
using ShuffleExtension;
using System.Threading;
using System.Data;
using MathSpace;
using CountExtension;
namespace Rextester
{

public class Program {
        
        public int ratio1;
        public int ratio2;
        public int ratio3;
        public int num1, num2, num3;
        
        public static void Main(String[] args){
            
           //makeMixedNum();
            //LCM(12,10,5);
            //LCM3Q();
            //makeDeciQ();
            
            //simultQ();
            //makeDivQ3by2();
            //addSub3Q();
            //makeOpQ();
            //RandomDie();
            makeMultQ(2,12,2,12);
            //addSubQ();
            //simult4x4();
            //simult3x3();
            
           // quadSeq();
        }
        
        public static void quadSeq() {
            
            int a, b, c;
            
            int count =0;
            
            while (count<10) {
                a = Rand.NextPM(1,5);
            b = Rand.NextPM(1,6);
            c = Rand.NextPM(1,10);
            
                if (a==1) {
                        Console.Write("n^2 "+b+"n "+c+" = ");
                    }
                else if (a==-1) {
                        Console.Write("-n^2 "+b+"n "+c+" = ");
                    }
                else
                Console.Write(a+"n^2 "+b+"n "+c+" = ");
                for (int n=1; n<6; n++) {

Console.Write(a*n*n+b*n+c+", ");

}
                Console.WriteLine();
                count++;
            }
            
        }
        
        public static void simult3x3() {
         
            double[] c = new double[12];
            int limit = 50;
            double x, y, z;
            int count = 0;
            while (count<1) {
            for (int i = 0; i<c.Length; i++) {
                c[i] = Rand.NextPM(1,10);
            }
            
            
            /*
            c[0] = 2; c[1] = 1; c[2] = -1; c[3] = 5;
            c[4] = 3; c[5] = -1; c[6] = 2; c[7] = -1;
            c[8] = 1; c[9] = -1; c[10] = -1; c[11] = 0;
            //
            c[0] = 1; c[1] = -3; c[2] = 3; c[3] = -4;
            c[4] = 2; c[5] = 3; c[6] = -1; c[7] = 15;
            c[8] = 4; c[9] = -3; c[10] = -1; c[11] = 19;
             */
            x = ( (c[10]*c[5]-c[6]*c[9])*(c[6]*c[3]-c[2]*c[7]) - (c[6]*c[1]-c[2]*c[5])*(c[10]*c[7]-c[6]*c[11]) )
                / ( (c[10]*c[5]-c[6]*c[9])*(c[6]*c[0]-c[2]*c[4]) - (c[6]*c[1]-c[2]*c[5])*(c[10]*c[4]-c[6]*c[8]) );
            y = ((c[6]*c[3]-c[2]*c[7]) - (c[6]*c[0]-c[2]*c[4])*x ) / (c[6]*c[1]-c[2]*c[5]);
            z = (c[3] - c[0]*x - c[1]*y ) / c[2];
            
            
            if ((x%1==0.5 || x%1==0) && (y%1==0.5 || y%1==0) && (z%1==0.5 || z%1==0) &&
                Math.Abs(x)<limit && Math.Abs(y)<limit && Math.Abs(z)<limit) {
                    for (int i = 0; i <c.Length; i++) {
                        //num[i] = Rand.NextPM(1,10);
                        Console.Write(c[i]+ " ");
                        if ((i+1)%4==0 && i>0) {
                            Console.WriteLine();
                            
                        }
                    }
                Console.WriteLine();
                Console.WriteLine("x, y, z = {0}, {1}, {2}", x,y,z);
                Console.WriteLine();
                count++;
                }
            }
            
        }
        
        public static void simult4x4() {
            
            double a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4,d1,d2,d3,d4,e1,e2,e3,e4;
            double w,x,y,z;
            int count = 0;
            int limit = 50;
            while (count<1) {
                int[] num = new int[20];
                for (int i = 0; i <num.Length; i++) {

num[i] = Rand.NextPM(0,10);
                    //Console.WriteLine(num[i]);
                }
                /*
                a1 = 2 ;b1 = -1;  c1 = 5; d1 = 1; e1 = -3;
                a2 = 3; b2 = 2; c2 = 2; d2 = -6; e2 = -32;
                a3 = 1; b3 = 3; c3 = 3; d3 = -1; e3 = -47;
                a4 = 5; b4 = -2; c4 = -3; d4 = 3; e4 = 20;
                //
                a1 = 3; b1 = 8; c1 = 9; d1 = 2; e1 = 1;
                a2 = 5; b2 = 2; c2 = 7; d2 = 3; e2 = 2;
                a3 = 6; b3 = 4; c3 = 3; d3 = 6; e3 = 1;
                a4 = 2; b4 = 2; c4 = 5; d4 = 6; e4 = 3;
                */
                a1 = Convert.ToDouble(num[0]);
                b1 = Convert.ToDouble(num[1]);
                c1 = Convert.ToDouble(num[2]);
                d1 = Convert.ToDouble(num[3]);
                e1 = Convert.ToDouble(num[4]);
                a2 = Convert.ToDouble(num[5]);
                b2 = Convert.ToDouble(num[6]);
                c2 = Convert.ToDouble(num[7]);
                d2 = Convert.ToDouble(num[8]);
                e2 = Convert.ToDouble(num[9]);
                a3 = Convert.ToDouble(num[10]);
                b3 = Convert.ToDouble(num[11]);
                c3 = Convert.ToDouble(num[12]);
                d3 = Convert.ToDouble(num[13]);
                e3 = Convert.ToDouble(num[14]);
                a4 = Convert.ToDouble(num[15]);
                b4 = Convert.ToDouble(num[16]);
                c4 = Convert.ToDouble(num[17]);
                d4 = Convert.ToDouble(num[18]);
                e4 = Convert.ToDouble(num[19]);

//Console.WriteLine("{0} {1} {2} {3} {4}",a1,b1,c1,d1,e1);

x = (( ( (d4*c3-d3*c4)*(d3*b2-d2*b3)-(d3*c2-d2*c3)*(d4*b3-d3*b4) ) * ( (d3*c2-d2*c3)*(d2*e1-d1*e2)-(d2*c1-d1*c2)*(d3*e2-d2*e3) )  )-( (d3*c2-d2*c3)*(d2*b1-d1*b2)-(d2*c1-d1*c2)*(d3*b2-d2*b3) ) * ( (d4*c3-d3*c4)*(d3*e2-d2*e3)-(d3*c2-d2*c3)*(d4*e3-d3*e4) ))
                     /
                    ( ( (d4*c3-d3*c4)*(d3*b2-d2*b3)-(d3*c2-d2*c3)*(d4*b3-d3*b4) ) * ( (d3*c2-d2*c3)*(d2*a1-d1*a2)-(d2*c1-d1*c2)*(d3*a2-d2*a3) ) - ( (d3*c2-d2*c3)*(d2*b1-d1*b2)-(d2*c1-d1*c2)*(d3*b2-d2*b3) )* ( (d4*c3-d3*c4)*(d3*a2-d2*a3)-(d3*c2-d2*c3)*(d4*a3-d3*a4) ) );

y = ( (d3*c2-d2*c3)*(d2*e1-d1*e2) - (d2*c1-d1*c2)*(d3*e2-d2*e3) - ( (d3*c2-d2*c3)*(d2*a1-d1*a2) - (d2*c1-d1*c2)*(d3*a2-d2*a3) )*x ) 
                / ( (d3*c2-d2*c3)*(d2*b1-d1*b2) - (d2*c1-d1*c2)*(d3*b2-d2*b3) );

z = (d3*e2-d2*e3-(d3*a2-d2*a3)*x-(d3*b2-d2*b3)*y ) / (d3*c2-d2*c3);

w = (e1-a1*x-b1*y-c1*z) / d1;

if ((x%1==0.5 || x%1==0) && (y%1==0.5 || y%1==0) && (z%1==0.5 || z%1==0) && (w%1==0.5 || w%1==0) && Math.Abs(x)<limit && Math.Abs(y)<limit && Math.Abs(z)<limit && Math.Abs(w)<limit) {
                    for (int i = 0; i <num.Length; i++) {
                        //num[i] = Rand.NextPM(1,10);
                        Console.Write(num[i]+ " ");
                        if ((i+1)%5==0 && i>0) {
                            Console.WriteLine();
                            
                        }
                    }
                    /*Console.WriteLine();
                    Console.WriteLine("{0} {1} {2} {3} {4}",a1,b1,c1,d1,e1);
                    Console.WriteLine("{0} {1} {2} {3} {4}",a2,b2,c2,d2,e2);
                    Console.WriteLine("{0} {1} {2} {3} {4}",a3,b3,c3,d3,e3);
                    Console.WriteLine("{0} {1} {2} {3} {4}",a4,b4,c4,d4,e4);
                    */
                    
                    Console.WriteLine("x, y, z, w = {0}, {1}, {2}, {3}", x,y,z,w);
                    Console.WriteLine();
                    count++;
                }
            }
        }
        public static void RandomDie() {
            
            int numerator = 0;
            for (int i = 0; i<10000; i++){
                int die = Rand.Next(1,7);
                if (die==1) { numerator++; }
                double result = (double) numerator/i;
                Console.WriteLine("{0}/{1} = {2}", numerator, i, result);
            }
            
        }
        
        public static void LCMQ() {
            
            List<string> lcmQ = new List<string>();
            int count=0;
            while(count<100) {
                int left = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (lcm(left,right)<120 && Fraction.GCD(left,right)!=1 && lcm(left,right)!=left && lcm(left,right)!=right) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + " and " + right + " lcm = " + lcm(left,right));
                    
                }
            }
            
            while (count>=100 && count<130) {
             
                int left = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (lcm(left,right)<120 && Fraction.GCD(left,right)==1 && Math.Abs(left-right)<20) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + " and " + right + " lcm = " + lcm(left,right));
                } 
            }
            
            lcmQ.Shuffle();
            Print(lcmQ,"Lowest Common Multiple (1)","Find the LCM (or lowest common multiple) of each pair of numbers",20);
            
        }
        
        public static void LCM3Q() {
            
            List<string> lcmQ = new List<string>();
            int count=0;
            while(count<100) {
                int left = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (lcm(left,right)<120 && Fraction.GCD(left,right)!=1 && lcm(left,right)!=left && lcm(left,right)!=right) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + " and " + right + " @lcm(" + left + "," + right + ")=" + lcm(left,right));
                    
                }
            }
            
            while (count>=100 && count<130) {
             
                int left = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (lcm(left,right)<120 && Fraction.GCD(left,right)==1 && Math.Abs(left-right)<20) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + " and " + right + " @lcm(" + left + "," + right + ")=" + lcm(left,right));
                } 
            }
            
            while(count<150) {
                int left = Rand.Next(2,100);
                int middle = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (left!=middle && middle!=right && lcm(left,middle,right)<120 && GCD(left,middle,right)!=1 && lcm(left,right)!=left && lcm(left,right)!=right) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + ", " + middle + ", " + right + " @lcm(" + left + "," + middle + "," + right + ")=" + lcm(left,middle,right));
                    
                }
            }
            
            while (count>=150 && count<170) {
             
                int left = Rand.Next(2,100);
                int middle = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (left!=middle && middle!=right && lcm(left,middle,right)<120 && GCD(left,middle,right)==1 && Math.Abs(max(left,middle,right)-min(left,middle,right))<20) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + ", " + middle + ", " + right + " @lcm(" + left + "," + middle + "," + right + ")=" + lcm(left,middle,right));
                } 
            }
            
            lcmQ.Shuffle();
            Print(lcmQ,"Lowest Common Multiple (3)","Find the LCM (or lowest common multiple) of each set of numbers",20);
        }
        
        public static void LCM2Q() {
            
            List<string> lcmQ = new List<string>();
            int count=0;
            while(count<100) {
                int left = Rand.Next(2,100);
                int middle = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (left!=middle && middle!=right && lcm(left,middle,right)<120 && GCD(left,middle,right)!=1 && lcm(left,right)!=left && lcm(left,right)!=right) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + ", " + middle + ", " + right + " @lcm(" + left + "," + middle + "," + right + ")=" + lcm(left,middle,right));
                    
                }
            }
            
            while (count>=100 && count<130) {
             
                int left = Rand.Next(2,100);
                int middle = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (left!=middle && middle!=right && lcm(left,middle,right)<120 && GCD(left,middle,right)==1 && Math.Abs(max(left,middle,right)-min(left,middle,right))<20) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + ", " + middle + ", " + right + " @lcm(" + left + "," + middle + "," + right + ")=" + lcm(left,middle,right));
                } 
            }
            
            lcmQ.Shuffle();
            Print(lcmQ,"Lowest Common Multiple (2)", "Find the LCM (or lowest common multiple) of each pair of numbers", 20);
        }
        
        public static void Reversal() { // finds the 4-digit reverse number
        
            for (int a = 0; a<10;a++){
                    
                    for (int b = 0; b<10;b++){
                    
                        for (int c = 0; c<10;c++){
                        
                            for (int d = 0; d<10;d++){
                                
                                double n = 9;
                                if ((n*1000*a+n*100*b+n*10*c+n*d)==(1000*d+100*c+10*b+a)) {
                                    
                                    Console.WriteLine(a+""+b+""+c+""+d);
                                }
                            }
                        }
                    }
                }
        
        }
        
        public static int Tens(){ // randomises 10 or 100
         
            int rand = Rand.Next(0,2);
            
            if (rand==0) {
                
                return 10;
                
            }
            
            else 
                
                return 100;
               
        }
        
        public static int Tens2() { // returns 1, 10 or 100 randomly
            
            int rand = Rand.Next(0,3);
            
            if (rand==0) {
                return 1;
            }
            
            else if (rand==1) {
                return 10;
            }
            
            else return 100;
               
        }
        
        public static void simpleArith() {
         
            int maxNum = 3600;
            //string title = "Addition \\& Subtraction (2 by 1 digits) $<$ "+ maxNum;
            string title = "Addition Speed Practice";
            
            List<string> questions = new List<string>();
            List<string> addQ = new List<string>();
            List<string> subQ = new List<string>();
            
            while(addQ.Count()<maxNum) {
                //int left = Rand.Next(11,70);
                //int right = Rand.Next(2,10);
                int left = Rand.Next(1,10);
                int right = Rand.Next(1,10);
                int result = left + right;
                if (result<=10) addQ.Add("        \\item \$"+left+"+"+right+"=\\underline{\\hspace{2cm}}\$");
            }
            
            while(subQ.Count()<maxNum) {
                int left = Rand.Next(11,70);
                int right = Rand.Next(2,10);
                subQ.Add("        \\item \$"+left+"-"+right+"=\\underline{\\hspace{2cm}}\$");
            }
            
            questions.AddRange(addQ);
            //questions.AddRange(subQ);
            questions.Shuffle();
            PrintArithmetic(questions, title,50);
            //PrintAnswerKey(questions, title, 30);
            
        }
        
         public static void addSub3TQ() { // add and sub 3 terms
            
             string title = "Addition \\& Subtraction (3 term) (2)";
             List<string> addsubQ = new List<string>();
             DataTable dt = new DataTable();
             int n1, n2, n3;
             
             for (int k=0; k<9000; k++){
                 int[] n = new int[3];
                 
                 n[0] = Rand.Next(101,1000);
                 n[1] = Rand.Next(11,1000);
                 n[2] = Rand.Next(11,1000);
                 int[] op = new int[2];
                 op[0] = Rand.Next(0,2);
                 op[1] = Rand.Next(0,2);
                 string[] operand = new string[2];
                 operand[0] = "+";
                 operand[1] = "-";
                 int result;
                 if (n[0]-n[1]>=0&& (n[0]-n[1])-n[2]>=0 && (n[0]+n[1]+n[2]<1000) && addsubQ.Count()<300){
                     
                     result = Convert.ToInt32(dt.Compute(n[0]+operand[op[0]]+n[1]+operand[op[1]]+n[2], null));
                     addsubQ.Add("        \\item \$\\mathmakebox[3.0cm][r]{"+n[0]+operand[op[0]]+n[1]+operand[op[1]]+n[2]+"}=\\underline{\\hspace{2cm}}\$");
                     //Console.WriteLine(result);
                 }
                
             }
             
             //Console.WriteLine(addsubQ.Count());
             //addsubQ.Shuffle();
             PrintArithmetic(addsubQ, title);
         
         }

public static void addSubQ() { // add and sub questions
            
            string title = "Addition \\& Subtraction (1)";
            string subtitle = "without carry over or borrowing";
            List<string> addQ = new List<string>();
            while (addQ.Count()<120) {
                    
                int i = Rand.Next(10,100);
                int j = Rand.Next(10,100);
                
                //if (i+j<100) addQ.Add("        \\item \$\\mathmakebox[1.5cm][r]{"+i+"+"+j+"}=\\underline{\\hspace{2cm}}\$"); //\\mathmakebox[1.45cm][r]{  
                if ((i/10+j/10)<10 && (i%10+j%10)<10) addQ.Add("        \\item \$\\mathmakebox[1.5cm][r]{"+i+"+"+j+"}=\\underline{\\hspace{2cm}}\$"); // for no carry over
            
            }
            
            List<string> subQ = new List<string>();

while (subQ.Count()<120) {
                
                int i = Rand.Next(10,100);
                int j = Rand.Next(10,100);
                
                //if (i>j && i%10>j%10) { subQ.Add("        \\item \$\\mathmakebox[1.5cm][r]{"+i+"-"+j+"}=\\underline{\\hspace{2cm}}\$");}
                if ((i/10>j/10) && (i%10>j%10)) subQ.Add("        \\item \$\\mathmakebox[1.5cm][r]{"+i+"-"+j+"}=\\underline{\\hspace{2cm}}\$");

}
            
            List<string> questions = new List<string>();
            //Console.WriteLine(addQ.Count());
            //Console.WriteLine(subQ.Count());
            addQ.Shuffle();
            subQ.Shuffle();
            questions.AddRange(addQ);
            questions.AddRange(subQ);
            questions.Shuffle();
            PrintArithmetic(questions, title, subtitle);
            
        }
        
        public static void addSub2Q() { // add and sub questions
            
            string title = "Addition \\& Subtraction (2 Digits)";
            List<string> addQ = new List<string>();
            while(addQ.Count()<150){
                    
                int i = Rand.Next(11,100);
                int j = Rand.Next(11,100);
                int result = i+j;
                        if (i+j<100) addQ.Add("        \\item \$"+i+"+"+j+"=\\underline{\\hspace{2cm}}\$"+result+"\\)"); //\\mathmakebox[1.45cm][r]{  
                    
                
            }
            
            List<string> subQ = new List<string>();
            while(subQ.Count()<150) {
                
                int i = Rand.Next(11,100);
                int j = Rand.Next(11,100);
                int result = i-j;
                                   
                if (i>j){subQ.Add("        \\item \$"+i+"-"+j+"=\\underline{\\hspace{2cm}}\$"+result+"\\)");}
                        
            }
            
            List<string> questions = new List<string>();
            //Console.WriteLine(addQ.Count());
            //Console.WriteLine(subQ.Count());
            addQ.Shuffle();
            subQ.Shuffle();
            questions.AddRange(addQ);
            questions.AddRange(subQ);
            questions.Shuffle();
            
            PrintArithmetic(questions, title);
            PrintAnswerKey(questions, title, 30);
            
        }
        
        public static void addSub3Q() { // add and sub questions
            
            string title = "Addition \\& Subtraction (3 Digits)";
            List<string> addQ = new List<string>();
            while(addQ.Count()<150){
                    
                int i = Rand.Next(101,1000);
                int j = Rand.Next(101,1000);
                int result = i+j;
                        if (i+j<1000) addQ.Add("        \\item \$"+i+"+"+j+"=\\underline{\\hspace{2cm}}\$"+result+"\\)"); //\\mathmakebox[1.45cm][r]{  
                    
                
            }
            
            List<string> subQ = new List<string>();
            while(subQ.Count()<150){
                
                int i = Rand.Next(101,1000);
                int j = Rand.Next(101,1000);
                int result = i-j;
                                   
                if (i>j){subQ.Add("        \\item \$"+i+"-"+j+"=\\underline{\\hspace{2cm}}\$"+result+"\\)");}
                        
            }
            
            List<string> questions = new List<string>();
            //Console.WriteLine(addQ.Count());
            //Console.WriteLine(subQ.Count());
            addQ.Shuffle();
            subQ.Shuffle();
            questions.AddRange(addQ);
            questions.AddRange(subQ);
            questions.Shuffle();
            
            PrintArithmetic(questions, title);
            PrintAnswerKey(questions, title, 30);
            
        }
        
        public static void multDivQ() { // mult and div questions
            
            string title = "Multplication \\& Division (1)";
            List<string> multQ = new List<string>();
            DataTable dt = new DataTable();
            for (int k=0; k<4; k++){
                    
                for (int i=2; i<=9; i++){
                                
                    for (int j=2; j<=9; j++){
                                   
                        if (multQ.Count()<200) multQ.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+i+"\\times"+j+"}=\\underline{\\hspace{2cm}}\$"); //\\mathmakebox[1.45cm][r]{  
                    }   
                }   
            }
            
            List<string> divQ = new List<string>();
            for (int k=0; k<4; k++){
                
                for (int i=10; i<=100; i++){

for (int j=2; j<=9; j++){
                        
                        if (divQ.Count()<200 && i>j && i%j==0 &&i/j<10){divQ.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+i+"\\div"+j+"}=\\underline{\\hspace{2cm}}\$");}
                        
                    }
        
                }
            }
            
            List<string> questions = new List<string>();
            //Console.WriteLine(multQ.Count());
            //Console.WriteLine(divQ.Count());
            
            questions.AddRange(multQ);
            questions.AddRange(divQ);
            questions.Shuffle();
            PrintArithmetic(questions, title);
            
        }

public static void makeMultQ(int lower1, int upper1, int lower2, int upper2) {
            
            string title = "Multiplication  (1)";
            List<string>[] questions = new List<string>[5];
            
            List<string> multQ = new List<string>();
            // the way this code works is it goes through all combinations of the times table without imbalance such as duplicates
            // or missing a particular question. the code goes through that in five loops and adds all the lists together before
            // printing them out.
            for (int k=0; k<5; k++){
                    
                questions[k] = new List<string>();
                
                for (int i=lower1; i<=upper1; i++){
                                
                    for (int j=lower2; j<=upper2; j++){
                                   
                        questions[k].Add("        \\item \$"+i+"\\times"+j+"=\\underline{\\hspace{2cm}}\$"); //\\mathmakebox[1.45cm][r]{  
                    }   
                }
                questions[k].Shuffle();
                multQ.AddRange(questions[k]);
            }
            
            PrintArithmetic(multQ, title);
            
        }
        
        
        
        /*List<int> listNumbers = new List<int>();
do
    {
        int numbers = rand.Next(1,49);
        if(!listNumbers.Contains(number)) {
            listNumbers.Add(numbers);
        }
    } while (listNumbers.Count < 6)
    
    */
        
		public static void makeMultQ3by1() {
            
            string title = "Multplication (3 by 1 Digits)";
            List<string> questions = new List<string>();
            for (int k=0; k<300; k++){
            
			int i = Rand.Next(101,1000);
			int j = Rand.Next(11,100);
			i = Rand.Next(101,1000);
			i = Rand.Next(101,1000);
			j = Rand.Next(2,10);
			j = Rand.Next(2,10);
				questions.Add("        \\item \$"+i+"\\times"+j+"=\\underline{\\hspace{2cm}}\$"); //\\mathmakebox[1.45cm][r]{  
            
            }
            
            questions.Shuffle();
            
            PrintArithmetic(questions, title);
            //Console.WriteLine(questions.Count());
        }
		
        public static void makeDivQ(int lower1, int upper1, int lower2, int upper2) {
            
            string title = "Division (2 by 1 digits) General";
            List<string> questions = new List<string>();
            for (int k=0; k<4; k++){
                
                for (int i=lower1; i<=upper1; i++){

for (int j=lower2; j<=upper2; j++){
                        
                        if (i>j){questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+i+"\\div"+j+"}=\\underline{\\hspace{2cm}}\$");}
                        
                    }
        
                }
            }
            questions.Shuffle();
            
            PrintArithmetic(questions, title);
            
        }
		
        public static void makeDivQ3by1() {
            
            string title = "Division (2 by 1 digits) General";
            List<string> questions = new List<string>();
            
            for (int k=0; k<100; k++) {
            int i = Rand.Next(101,1000);
            int j = Rand.Next(2,10);
            
                if (i>j){questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+i+"\\div"+j+"}=\\underline{\\hspace{2cm}}\$");}

}
            questions.Shuffle();
            
            PrintArithmetic(questions, title);
            
        }
        
        
		public static void makeDivQ3by2() {
            
            string title = "Division (3 by 2 digits)";
            List<string> questions = new List<string>();
            
            while(questions.Count()<150) {
                int i = Rand.Next(101,1000);
                int j = Rand.Next(11,100);
                int result = i/j;
                if (i>j && i%j==0) { questions.Add("        \\item \$"+i+"\\div"+j+"=\\underline{\\hspace{2cm}}\$"+result+"\\)"); }

}
            questions.Shuffle();
            
           // PrintArithmetic(questions, title);
            
            PrintAnswerKey(questions, title, 30);
            
        }
        
        public static void makeDeciQ(){
            
            string title = "Decimal Arithmetic General";
            // Division
            List<string> divQ = new List<string>();
            for (int i=0; i<6500; i++) {
                int tens = Tens();
                double argument = Math.Truncate(Rand.NextD(1.0,99.99)*tens)/tens;
                
                decimal num1 = Rand.Next(2,100);
                int dividend = Rand.Next(2,1000);
                decimal result = dividend/num1;
                int count = BitConverter.GetBytes(decimal.GetBits(result)[3])[2];
                
                //Console.WriteLine(count);
                if(count<4 && divQ.Count()<120) {
                    //Console.WriteLine("{0}/{1}={2}", dividend,num1, dividend/num1);
                    divQ.Add("        \\item \$\\mathmakebox[3cm][r]{"+dividend+"\\div"+num1+"}=\\underline{\\hspace{2cm}}\$");
                }
                
                
            }
            
            //Multiplication
            List<string> multQ = new List<string>();
            
            for (int i=0; i<120; i++) {
                double number = Rand.NextD(1.0,99.99);
                int hund;
                double num1;
                if (number>=10) {
                    num1 = Math.Truncate(number*10)/10;
                    hund = 10;
                }
                
                else {
                    num1 = Math.Truncate(number*100)/100;
                    hund = 10;
                }
                
                double num2 = Math.Truncate(Rand.NextD(2,hund)*hund)/hund;
                double result = num1*num2;
                if ( (Math.Floor(num1)!=num1 || Math.Floor(num2)!=num2) && multQ.Count()<120) {
                    multQ.Add("        \\item \$\\mathmakebox[3cm][r]{"+num1+"\\times"+num2+"}=\\underline{\\hspace{2cm}}\$");
                }
            }
            
            //Add
            List<string> addQ = new List<string>();
            
            for (int i=0; i<120; i++) {
                double number = Rand.NextD(1.0,99.99);
                int hund = Tens();
                double num1;
                if (number>=10) {
                    num1 = Math.Truncate(number*10)/10;
                    //hund = 100;
                }
                
                else {
                    num1 = Math.Truncate(number*100)/100;
                    //hund = 10;
                }
                
                double num2 = Math.Truncate(Rand.NextD(2,hund)*hund)/hund;
                double result = num1+num2;
                addQ.Add("        \\item \$\\mathmakebox[3cm][r]{"+num1+"+"+num2+"}=\\underline{\\hspace{2cm}}\$");
            }
            
            //Subtract
            List<string> subQ = new List<string>();
            
            for (int i=0; i<300; i++) {
                double number = Rand.NextD(1.0,99.99);
                int hund = Tens();
                double num1;
                if (number>=10) {
                    num1 = Math.Truncate(number*10)/10;
                    //hund = 100;
                }
                
                else {
                    num1 = Math.Truncate(number*100)/100;
                    //hund = 10;
                }
                
                double num2 = Math.Truncate(Rand.NextD(2,hund)*hund)/hund;
                if(num1>num2) {
                    double result = num1-num2;
                    subQ.Add("        \\item \$\\mathmakebox[3cm][r]{"+num1+"+"+num2+"}=\\underline{\\hspace{2cm}}\$");
                }
                
            }
            List<string> questions = new List<string>();
            //questions.AddRange(addQ);
            //questions.AddRange(subQ);
            questions.AddRange(multQ);
            //questions.AddRange(divQ);
            
            questions.Shuffle();
            PrintArithmetic(questions,title);
        }
        
        public static void makeDeciDivQ() {
         
            string title = "Decimal Division General";
            // Division
            List<string> divQ = new List<string>();
            for (int i=0; i<6500; i++) {
                int tens = Tens();
                
                
                decimal divisor = (decimal) Rand.Next(2,100)/Tens2();
                decimal dividend = (decimal) Rand.Next(2,1000)/Tens2();
                decimal result = dividend/divisor;
                int resultInt = Convert.ToInt32(result);
                int count = BitConverter.GetBytes(decimal.GetBits(result)[3])[2];
                
                //Console.WriteLine(count);
                if(count<4 && divQ.Count()<120) {
                    //Console.WriteLine("{0}/{1}={2}", dividend,num1, dividend/num1);
                    divQ.Add("        \\item \$\\mathmakebox[3cm][r]{"+dividend+"\\div"+divisor+"}=\\underline{\\hspace{2cm}}\$");
                }
                //if (divisor!=1 && count<4 && resultInt.Count()<4) Console.WriteLine(dividend+ " / " +divisor + " = " + result);
//                if (count<4 && resultInt.Count()<4 ) Console.WriteLine((int)result);
                if (
                    !(BitConverter.GetBytes(decimal.GetBits(divisor)[3])[2]==0 && BitConverter.GetBytes(decimal.GetBits(dividend)[3])[2]==0 
                      && BitConverter.GetBytes(decimal.GetBits(result)[3])[2]==0) && divisor!=1 && count<4 && divQ.Count()<120) {
                
                      
                    Console.WriteLine(dividend+ " / " +divisor + " = " + result);
                }
            
            
        
            }
        
        }
              
        /*public static void makeDeciQ(double upper1) {
            
            string title = "Division (2 by 1 digits) General";
            List<string> addquestions = new List<string>();
            List<string> subquestions = new List<string>();
            List<string> multquestions = new List<string>();
            List<string> divquestions = new List<string>();
            string[] op = new string[4] {"+", "-", "\\times", "\\div"};

for (int i=1; i<=upper1; i++){
                
                int operand = Rand.Next(1,4);
                double[] num = new double[2] {Math.Truncate(Rand.NextD(1.0,99.99)*100)/100, Rand.Next(2,999)};
                
                decimal num1 = Convert.ToDecimal(num[1]));
                //if (operand==2){questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+num[0]+op[operand]+num[1]+"}=\\underline{\\hspace{2cm}}\$");}
                    
                
                if (operand==4 && num[2]%num1==0){questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+num[0]+op[operand]+num[1]+"}=\\underline{\\hspace{2cm}}\$");}
                    
                //else if (operand==1) {questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+num[0]+op[operand]+num[1]+"}=\\underline{\\hspace{2cm}}\$");}
                //else if (operand==3) {questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+num[0]+op[operand]+num[1]+"}=\\underline{\\hspace{2cm}}\$");}
            }
            
            //questions.Shuffle();
            
            //PrintArithmetic(questions, title);
            
        }*/
                                    
        public static void makeSubQ2by2(int lower1, int upper1, int lower2, int upper2){
            
			string title = "Subtraction (2 by 2 Digits)";
            string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{2em}"};
            
            string[] op = new string[2] {"(", ")("};
            string end =")=\\)";
            
            List<string> questions = new List<string>();
            
            for (int i=lower1; i<=upper1; i++){
            //for (int i=10; i<100;i++){
                
                for (int j=lower2; j<=upper2; j++){
                //for (int j=10; j<100;j++){   
                   
                    if (i!=j && i+j<100){questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+i+"-"+j+"}=\\underline{\\hspace{2cm}}\$");}
                   /*if (i>j) {
                       
                       questions.Add("        \\item \$"+i+"-"+j+"=\$");
                       
                   }*/
                   
                }
                
            }
            questions.Shuffle();
            
            //Console.WriteLine(questions.Count());
            
            PrintArithmetic(questions, title);
            /*for (int i=0; i<questions.Count(); i++){
                
                if(i==0){

Console.WriteLine("\\begin{figure}[ht!]");
                    Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                    Console.WriteLine("\\end{figure}");
                    Console.WriteLine();
                    Console.WriteLine("\\vspace{-15mm}\\begingroup");
                    Console.WriteLine("\\centering");
                    Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                    //Console.WriteLine("\\large Promatics Education Centre\\\\[1.5em]");
                    Console.WriteLine("\\endgroup");
                    Console.WriteLine();
                    Console.WriteLine(latex[0]);
                    Console.WriteLine("\\textbf{Exercise "+(i/30+1)+". "+exerciseTitle+".}\\\\");
                    Console.WriteLine("\\begin{multicols}{2}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                    Console.WriteLine(latex[1]);

}
                Console.WriteLine(questions[i]);
               
                if (i!=0 && (i+1)%30==0){
                  
                    
                    Console.WriteLine("\\end{enumerate}");
                    Console.WriteLine("\\end{multicols}");
                    Console.WriteLine();
                    Console.WriteLine("\\pagebreak[4]");
                    Console.WriteLine();
                    Console.WriteLine("\\begin{figure}[ht!]");
                    Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                    Console.WriteLine("\\end{figure}");
                    Console.WriteLine();
                    Console.WriteLine("\\vspace{-15mm}\\begingroup");
                    Console.WriteLine("\\centering");
                    Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                    //Console.WriteLine("\\large Promatics Education Centre\\\\[1.5em]");
                    Console.WriteLine("\\endgroup");
                    Console.WriteLine();
                    Console.WriteLine(latex[0]);
                    Console.WriteLine("\\textbf{Exercise "+((i+30)/30+1)+". "+exerciseTitle+".}\\\\");
                    Console.WriteLine("\\begin{multicols}{2}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                    Console.WriteLine(latex[1]);
                }
            }*/
        }
        
        public static void makeAddQ2by1(int lower1, int upper1, int lower2, int upper2){
            
			string title = "Subtraction (2 by 2 Digits)";
            string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{2em}"};
            
            string[] op = new string[2] {"(", ")("};
            string end =")=\\)";
            
            List<string> questions = new List<string>();
            
            for (int i=lower1; i<=upper1; i++){
            //for (int i=10; i<100;i++){
                
                for (int j=lower2; j<=upper2; j++){
                //for (int j=10; j<100;j++){   
                   
                    questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+i+"+"+j+"}=\\underline{\\hspace{2cm}}\$");
                   /*if (i>j) {
                       
                       questions.Add("        \\item \$"+i+"-"+j+"=\$");
                       
                   }*/
                   
                }
                
            }
            questions.Shuffle();
            
            PrintArithmetic(questions, title);
           
        }
		
        public static void makeAlg() { // algebraic questions
            
            int[] n = new int[10];
            
            for (int j=0; j<50; j++) {
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(1,10);
                }
                char[] op = new char[] {'+','-'};
                int x = Rand.Next(0,2);
                int y = Rand.Next(0,2);
                int z = Rand.Next(0,2);
                Console.WriteLine("\$\\dfrac{{{7}(x{4}{0})}}{{{1}}}{6}\\dfrac{{{8}(x{5}{2})}}{{{3}}}=\$\\\\",n[0],n[1],n[2],n[3],op[x],op[y],op[z],n[4],n[5]);
            }

}

public static void makeQ(int lower1, int upper1, int lower2, int upper2){
         
            for (int i=lower1; i<=upper1; i+=9){

for (int j=lower2; j<=upper2; j+=9){

Console.WriteLine("        \\item \$"+i+"\\operation"+j+"=\$");                   
            
                }
              
            }

}
        
        public static void makeFracQ(){
        
            string title = "Algebra Simplification Introduction";
            string exerciseTitle = "Simplify the algebraic expressions";
            int m=0;
            int i_final=30000;
            int incre= 0;
            
            string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{2em}"};
            string mathbox = "\\mathmakebox[1.45cm][r]{";
            string[] op = new string[2] {"(", ")("};
            string end =")=\\)";
            
            List<string> questions = new List<string>();
            
            
            //for (int i=lower1; i<=upper1; i+=9){
            for (int i=1; i<100;i++){
                
                //for (int j=lower2; j<=upper2; j+=9){
                for (int j=10; j<100;j++){   
                    
                    int num1 = Rand.Next(1,10);
                    int num2 = Rand.Next(1,10);
                    int denom1 = Rand.Next(2,10);
                    int denom2 = Rand.Next(2,10);
                    int mixed1 = Rand.Next(0,10);
                    int mixed2 = Rand.Next(0,10);
                    
                    if (num1!=denom1 && num2!=denom1 && num1<denom1 && num2<denom1){questions.Add("        \\item \$"+mixed1+"\\dfrac{"+num1+"}{"+denom1+"}+"+mixed2+"\\dfrac{"+num2+"}{"+denom1+"}=\\underline{\\hspace{2cm}}\$");}
                   /*if (i>j) {
                       
                       questions.Add("        \\item \$"+i+"-"+j+"=\$");
                       
                   }*/
                   
                }
                
            }
            questions.Shuffle();
            
            //Console.WriteLine(questions.Count());
            
            for (int i=0; i<questions.Count(); i++){
                
                if(i==0){

}
                    
                }
               
            }
             
        }*/

public static void makeAlgebra(){
        
            //string[] vari = new string[24] {"a","b","c","d","f","g","h","k","m","n","p","q","r","s","t","u","v","w","x","y","z","\\delta", "\\epsilon", "\\phi"};
            string[] vari = new string[21] {"a","b","c","ab","bc","ac","abc","x","y","z","xy","yz","xz","xyz","k","m","n","km","kn","mn","kmn"};
            //var[0] = "a";
            //var[1] = "b";
            //var[2] = "c";
            
            int n=-1; // n is the random number of variables per question
            int m=0;
            int i_final=30000;
            int incre= 0;
            string title = "Algebra Simplification Introduction";
            string exerciseTitle = "Simplify the algebraic expressions";
            string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{2em}"};
            
            string[] op = new string[4] {"+","-","(", ")("};
            int operand = Rand.Next(0,1);
            //string end =")=\\)";
            string end = "=\\)";
            for (int i=1; i<=i_final; i++) {

int num2=Rand.Next(0,7);  // range of number of different variables per question
                int num = Rand.Next(2,5); // range of number of total variables per question
                int consts=Rand.Next(-9,10); // range of coefficients of the variables
                while (true) {
                    consts=Rand.Next(-9,10);
                    if (consts==0) {
                        consts=Rand.Next(-9,10);
                    }
                    else break;
                }
                if(i==1){

Console.WriteLine("\\begin{figure}[ht!]");
                    Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                    Console.WriteLine("\\end{figure}");
                    Console.WriteLine();
                    Console.WriteLine("\\vspace{-15mm}\\begingroup");
                    Console.WriteLine("\\centering");
                    Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                    //Console.WriteLine("\\large Promatics Education Centre\\\\[1.5em]");
                    Console.WriteLine("\\endgroup");
                    Console.WriteLine();
                    Console.WriteLine(latex[0]);
                    Console.WriteLine("\\textbf{Exercise "+(m/30+1)+". "+exerciseTitle+".}\\\\");
                    Console.WriteLine("\\begin{multicols}{2}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                    Console.WriteLine(latex[1]);

}

if (n==-1){ //first variable of each question
                    Console.Write("        \\item \\(");
                }
                
                if (n==0){
                Console.Write(consts+vari[num2+7*incre]+op[operand]);
                
                }
            
                else if (n>0 && n<num){
                    Console.Write(consts+vari[num2+7*incre]+op[operand]);
                }
                n++;                
                if (n==num){ 
                    m++;
                    Console.Write(consts+vari[num2+7*incre]);
                    Console.Write(end);
                    Console.WriteLine();
                    
                    if (m%30==0) {
                        incre=Rand.Next(0,3);
                        Console.WriteLine("\\end{enumerate}");
                        Console.WriteLine("\\end{multicols}");
                        Console.WriteLine();
                        Console.WriteLine("\\pagebreak[4]");
                        Console.WriteLine();
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        //Console.WriteLine("\\large Promatics Education Centre\\\\[1.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        Console.WriteLine(latex[0]);
                        Console.WriteLine("\\textbf{Exercise "+(m/30+1)+". "+exerciseTitle+".}\\\\");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
                    }
                    
                    Console.Write("        \\item \\(");
                    n=0;
                }
                
                else if (n>num){
                    m++;
                    Console.Write(consts+vari[num2+3*incre]);
                    Console.Write(end);
                    Console.WriteLine();
                    
                    if (m%30==0) {
                        incre=Rand.Next(0,3);
                        Console.WriteLine("\\end{enumerate}");
                        Console.WriteLine("\\end{multicols}");
                        Console.WriteLine();
                        Console.WriteLine("\\pagebreak[4]");
                        Console.WriteLine();
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        //Console.WriteLine("\\large Promatics Education Centre\\\\[1.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        Console.WriteLine(latex[0]);
                        Console.WriteLine("\\textbf{Exercise "+((m+30)/30+1)+". "+exerciseTitle+".}\\\\");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
                    }
                    
                    Console.Write("        \\item \\(");
                    n=0;
                }

/* if(i==i_final){
                    Console.WriteLine("\\end{enumerate}");
                    Console.WriteLine("\\end{multicols}");
                    
                }*/

}
            
            
        }
        
     
        public static void makeDiv4by2()     {
            
            for (int i =0; i<10000; i++) {
                  
                int dividend = Rand.Next(1001,10000);
                int divisor = Rand.Next(11,99);

if (dividend%divisor==0) {
                Console.WriteLine("        \\item \$"+dividend+"\\div"+divisor+"=\$");
                    
                }
            }
        }
        
        public static void makeSciNot(){
            
            for (int i=0; i<100; i++){
                
                int num1 = Rand.Next(1,10);
                int dec1 = Rand.Next(1,10);
                int num2 = Rand.Next(1,10);
                int dec2 = Rand.Next(1,10);
                int exp = Rand.Next(-9,10);
                int plusminus = Rand.Next(-1,2);
                if (num1>num2 && exp != exp+plusminus){
                    
                Console.WriteLine("        \\item \${0}.{3} \\times 10^{{{2}}}+{1}.{4} \\times 10^{{{5}}}=\$",num1,num2,exp,dec1,dec2,exp+plusminus);
                }
            }
        }
        
        public static void DN(){
            
            //st<string> sign = new List<string>(new string[] {"+","-","*","/"});
            List<char> sign = new List<char>(new char[] {'+','-','*','/'});
            
            for (int i=0;i<100;i++){
                
                string question = "{0}{1}{2}{3}{4}{5}{6}";
                int pick1= Rand.Next(0+sign.Count());
                int pick2= Rand.Next(0+sign.Count());
                int pick3= Rand.Next(0+sign.Count());
                int num1=Rand.Next(-9,10);
                int num2=Rand.Next(-9,10);
                int num3=Rand.Next(-9,10);
                int num4=Rand.Next(-9,10);
                string num1_str, num2_str, num3_str, num4_str;
                bool num1_b = num1<0;
                bool num2_b = num2<0;
                bool num3_b = num3<0;
                bool num4_b = num4<0;
                
                if (num1_b && !num2_b && !num3_b && !num4_b) {
                    num1_str = "("+num1.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2,sign[pick2],num3,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                    
                }
                
                else if (num2_b && !num1_b && !num3_b && !num4_b){
                    num2_str = "("+num2.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2_str,sign[pick2],num3,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num3_b && !num1_b && !num2_b && !num4_b){
                    num3_str = "("+num3.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2,sign[pick2],num3_str,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num4_b && !num1_b && !num2_b && !num3_b){
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2,sign[pick2],num3,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num1_b && num2_b &&!num3_b && !num4_b){
                    num1_str = "("+num1.ToString()+")";
                    num2_str = "("+num2.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2_str,sign[pick2],num3,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num1_b && num3_b && !num2_b && !num4_b){ 
                    num1_str = "("+num1.ToString()+")";
                    num3_str = "("+num3.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2,sign[pick2],num3_str,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num1_b && num4_b && !num2_b && !num3_b){
                    num1_str = "("+num1.ToString()+")";
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2,sign[pick2],num3,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num2_b && num3_b && !num1_b && !num4_b){
                    num2_str = "("+num2.ToString()+")";
                    num3_str = "("+num3.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2_str,sign[pick2],num3_str,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num2_b && num4_b && !num1_b && !num3_b){
                    num2_str = "("+num2.ToString()+")";
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2_str,sign[pick2],num3,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num3_b && num4_b && !num1_b && !num2_b){
                    num3_str = "("+num3.ToString()+")";
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2,sign[pick2],num3_str,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num1_b && num2_b && num3_b && !num4_b){
                    num1_str = "("+num1.ToString()+")";
                    num2_str = "("+num2.ToString()+")";
                    num3_str = "("+num3.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2_str,sign[pick2],num3_str,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num1_b && num3_b && num4_b && !num2_b){
                    num1_str = "("+num1.ToString()+")";
                    num3_str = "("+num3.ToString()+")";
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2,sign[pick2],num3_str,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num1_b && num2_b && num4_b && !num3_b){
                    num1_str = "("+num1.ToString()+")";
                    num2_str = "("+num2.ToString()+")";
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2_str,sign[pick2],num3,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num2_b && num3_b && num4_b && !num1_b){
                    num2_str = "("+num2.ToString()+")";
                    num3_str = "("+num3.ToString()+")";
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2_str,sign[pick2],num3_str,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else {
                    Console.WriteLine(question,num1,sign[pick1],num2,sign[pick2],num3,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
              
            }

}
        
        public static void makeMixedNum() {
            
            int numQ = 150;
            int[] n = new int[10];
            List<string> questions = new List<string> ();
            
            //Add
            List<string> addQ = new List<string> ();
            
            while (addQ.Count()<numQ) {
                //n[0] = Rand.Next(10,400); // for prime factorization

int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                int y = Rand.Next(0,2);
                int z = Rand.Next(0,2);
                //Console.WriteLine("\$"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+op[x]+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}=\$");
                if (n[1]!=n[3] && n[0]<n[1] && n[2]<n[3]) {
                    double n0 = (double)n[0];
                    double n1 = (double)n[1];
                    double n2 = (double)n[2];
                    double n3 = (double)n[3];

Fraction left = new Fraction(n[4],n[0],n[1]);
                    Fraction right = new Fraction(n[5],n[2],n[3]);
                    Fraction result = (left + right).toMixed().Simplify();
                    // if the result is small enough (denominator <=20)
                    if (result.denom <= 20 && result.integer<=20 && n[0]!=n[1] && n[2]!=n[3]) {

if (result.integer!=0) {
                            if (result.num!=0) {
                                addQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+"}"+"+"+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.integer+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                            }
                            else addQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+"}"+"+"+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.integer+"\\)");
                        }
                        else addQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+"}"+"+"+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");

}
                }
            }
                        
            //Sub
            List<string> subQ = new List<string> ();
            
            while (subQ.Count()<numQ) {
                //n[0] = Rand.Next(10,400); // for prime factorization

int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

if (result.integer!=0) {
                            if (result.num!=0) {
                                subQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+"}"+"-"+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.integer+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                            }
                            else subQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+"}"+"-"+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.integer+"\\)");
                        }
                        else subQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+"}"+"-"+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");

}
                }
            }
            
            //Mult
            List<string> multQ = new List<string> ();
            
            int q = numQ/2;
            int m = 5;
            int m2 = 15;
            
            while (multQ.Count()<q/m) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                }
            }
            
            while (multQ.Count()<q+(q/m2)*2) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                    
                }
            }
            
                    
            
            while (multQ.Count()<q+(q/m2)*3) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                }
            }
                    
            
            while (multQ.Count()<q+(q/m2)*4) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                }
            }
                    
            
            while (multQ.Count()<q+(q/m2)*5) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                }
            }
            
            while (multQ.Count()<q+(q/m2)*6) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                    else if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                }
            }
        
            while (multQ.Count()<q+(q/m2)*7) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                                       
                }
            }

while (multQ.Count()<q+(q/m2)*8) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                    
                }
            }
            
            while (multQ.Count()<q+(q/m2)*9) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                    else if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                                       
                }
            }
            
            while (multQ.Count()<q+(q/m2)*10) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                    
                }
            }
                
            while (multQ.Count()<q+(q/m2)*11) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                    
                }
            }
            
            while (multQ.Count()<q+(q/m2)*12) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                                       
                }
            }
			
			while (multQ.Count()<q+(q/m2)*13) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                                       
                }
            }
			
			while (multQ.Count()<q+(q/m2)*14) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                                       
                }
            }
			while (multQ.Count()<q+(q/m2)*15) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        multQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                                       
                }
            }
			
            
            
            //Div
            List<string> divQ = new List<string> ();
            
            int q1 = numQ/2;
            int k = 5;
            int k2 = 15;
            
            while (divQ.Count()<q1/k) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                }
            }
            
            while (divQ.Count()<q1+(q1/k2)*2) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                    
                }
            }
            
                    
            
            while (divQ.Count()<q1+(q1/k2)*3) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                }
            }
                    
            
            while (divQ.Count()<q1+(q1/k2)*4) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                }
            }
                    
            
            while (divQ.Count()<q1+(q1/k2)*5) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div\\dfrac{"+n[2]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                }
            }
            
            while (divQ.Count()<q1+(q1/k2)*6) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                    else if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                }
            }
        
            while (divQ.Count()<q1+(q1/k2)*7) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                                       
                }
            }

while (divQ.Count()<q1+(q1/k2)*8) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                    
                }
            }
            
            while (divQ.Count()<q1+(q1/k2)*9) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                    else if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                                       
                }
            }
            
            while (divQ.Count()<q1+(q1/k2)*10) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                    
                }
            }
                
            while (divQ.Count()<q1+(q1/k2)*11) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                    
                }
            }
            
            while (divQ.Count()<q1+(q1/k2)*12) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                                       
                }
            }
			
			while (divQ.Count()<q1+(q1/k2)*13) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                                       
                }
            }
			
			while (divQ.Count()<q1+(q1/k2)*14) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                                       
                }
            }
			while (divQ.Count()<q1+(q1/k2)*15) {
                    
                int size = 99;

List<int> list = new List<int>(size);

for(int i = 1; i <= size; i++) {
                    list.Add(i);
                }

//while(list.Count() > 0) {
                for (int i=0; i<n.Count(); i++) {
                    int index = Rand.Next(list.Count());
                    n[i] = list[index];
                    list.RemoveAt(index);
                }
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom!=1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                    else if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3] && result.denom==1) {
                    
                        divQ.Add("        \\item \$\\mathmakebox[2.05cm][r]{"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\div"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}}="+"\\underline{\\hspace{3cm}\\vphantom{\\dfrac{1}{2}}}\$"+result.num+"\\)");
                    }
                                       
                }
            }
            
            //questions.AddRange(addQ);
            //questions.AddRange(subQ);
            questions.AddRange(multQ);
            questions.AddRange(divQ);
            questions.Shuffle();
            string title = "Fraction Multiplication \\& Division (General)";
            string exerciseTitle = "Leave your +/- answers in simplest Mixed Number form and $\\times/\\div$ in Improper Fraction form unless otherwise instructed";
            PrintFraction(questions, title, exerciseTitle);
            PrintAnswerKey(questions, title, 20);

}
        
        public static Fraction[] simultF(int[] c, int[] d) {
            
            Fraction x, y;
           //int[] c = new int[3];
           //int[] d = new int[3];
            if(c.Length != 3 && d.Length!=3)
               throw new ArgumentException("array should be int[3]");

int yLeft = c[0]*d[2]-d[0]*c[2];
            int yRight = c[0]*d[1]-d[0]*c[1];
            y = new Fraction(yLeft, yRight);
            
            Fraction xLeft = c[2]-c[1]*y;
            int xRight = c[0];
            x = new Fraction(xLeft,xRight);
            
            Fraction[] z = new Fraction[] {x,y};
            //Console.WriteLine("x = {0}, y = {1}",x,y); 
            return z;
            
        }
        
        public static double[] simultD(int[] c, int[] d) {
            
            double x,y;
           //int[] c = new int[3];
           //int[] d = new int[3];
            if(c.Length != 3 && d.Length!=3)
               throw new ArgumentException("array should be int[3]");
            
            y = (double) (c[0]*d[2]-d[0]*c[2] ) / (c[0]*d[1]-d[0]*c[1]);
            x = (double) (c[2]-c[1]*y)/c[0];
            
            double[] z = new double[] {x,y};
            //Console.WriteLine("x = {0}, y = {1}",x,y); 
            return z;
        }
        
        public static void simultQ() {
            
            int[] c = new int[6];
            int count = 0;
            
            List<string> questions = new List<string>();
            
            int[] numArray = new int[] {-9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9};
            while (questions.Count()<100 || count <100 ) {
            
                for (int i = 0; i<c.Length; i++) {

c[i] = numArray[Rand.Next(1,17)];
                }

if (c[0]*c[4]!=c[3]*c[1]) {

Fraction[] result = simultF(new int[] {c[0], c[1], c[2]}, new int[] {c[3], c[4], c[5]});
                    Fraction parse;
                    // 
                    //if (Math.Abs(result[0]*result[1])<200 && result[0]%1==0 && result[1]%1==0 && result[0]+result[1]!=0 && result[0]*result[1]!=0) {
                    if (Math.Abs((result[0]*result[1]).toDeci())<200 && result[0].Num+result[1].Num!=0 && result[0].Num*result[1].Num!=0 && Math.Abs(result[0].num)<10 && Math.Abs(result[0].denom)<10 && Math.Abs(result[1].num)<10 && Math.Abs(result[1].denom)<10) {
                        count++;
                        if (c[1]<0 && c[4]>0) {
                            // if x is a fraction but y is not
                            if (Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+result[1].Simplify()+"$"); 
                            }
                            
                            // if x is not a fraction but y is
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            
                            // if x and y are fractions
                            else if (Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                            }
                            //questions.Add(c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]);
                            //questions.Add(c[3]+"x + "+ c[4]+"y &= "+c[5]);
                            //questions.Add("\\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                        }
                        
                        else if (c[1]>0 && c[4]<0) {
                            // if x is a fraction but y is not
                            if (Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+result[1].Simplify()+"$"); 
                            }
                            
                            // if x is not a fraction but y is
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            
                            // if x and y are fractions
                            else if (Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                            }
                            //questions.Add(c[0]+"x + "+ c[1]+"y &= "+c[2]);
                            //questions.Add(c[3]+"x - "+ Math.Abs(c[4])+"y &= "+c[5]);
                            //questions.Add("\\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                        }
                        
                        else if (c[1]<0 && c[4]<0) {
                            // if x is a fraction but y is not
                            if (Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+ Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+result[1].Simplify()+"$"); 
                            }
                            
                            // if x is not a fraction but y is
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+ Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            
                            // if x and y are fractions
                            else if (Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+ Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+ Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                            }
                            //questions.Add(c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]);
                            //questions.Add(c[3]+"x - "+ Math.Abs(c[4])+"y &= "+c[5]);
                            //questions.Add("\\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                        }
                        
                        else {
                            // if x is a fraction but y is not
                            if (Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+result[1].Simplify()+"$"); 
                            }
                            
                            // if x is not a fraction but y is
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            
                            // if x and y are fractions
                            else if (Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$"); 
                            }
                            //questions.Add(c[0]+"x + "+ c[1]+"y &= "+c[2]);
                            //questions.Add(c[3]+"x + "+ c[4]+"y &= "+c[5]);
                            //questions.Add("\\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                        }
                    }
                }
            } 
            questions.Shuffle();
            string title = "Simultaneous Equations";
            string exerciseTitle = "Solve for $x$ and $y$";
            Print(questions, title, exerciseTitle, 20);
            
        }
        
        /*****************************************************
        /////////////////////LATEX CODES//////////////////////
        *****************************************************/
        
        public static void PrintArithmetic<T>(List<T> list, string title) {
        
        //string title = "Title ()";
        //string exerciseTitle = "Instructions";
        //int m=0;
        //int i_final=30000;
        //int incre= 0;
        
        string[] latex = new string[] {"\\fontsize{16pt}{25pt}\\selectfont", "        \\setlength\\itemsep{10pt}"};
        
        string[] op = new string[2] {"(", ")("};
        //string end = ")=\\)";
        
        for (int i=0; i<list.Count(); i++){
                    
                    if(i==0){
    
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\begingroup");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\end{center}");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        Console.WriteLine(latex[0]);
                        //Console.WriteLine("\\subsection{Exercise "+(i/30+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*), align=center,leftmargin=40pt]");
                        Console.WriteLine(latex[1]);
    
                    
                    }
                    Console.WriteLine(list[i]);
                   
                    if (i!=0 && (i+1)%30==0){
                      
                        
                        Console.WriteLine("    \\end{enumerate}");
                        Console.WriteLine("\\end{multicols}");
                        Console.WriteLine("\\end{center}");
                        Console.WriteLine();
                        Console.WriteLine("\\newpage");
                        Console.WriteLine();
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-33mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\hspace*{-10mm}\\begingroup");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\end{center}");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        //Console.WriteLine("\\subsection{Exercise "+((i+30)/30+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*), align=center,leftmargin=40pt]");
                        Console.WriteLine(latex[1]);
                    }
                }
        }
        
        public static void PrintArithmetic<T>(List<T> list, string title, string subtitle) {
        
        //string title = "Title ()";
        //string exerciseTitle = "Instructions";
        //int m=0;
        //int i_final=30000;
        //int incre= 0;
        
        string[] latex = new string[] {"\\fontsize{16pt}{25pt}\\selectfont", "        \\setlength\\itemsep{10pt}"};
        
        string[] op = new string[2] {"(", ")("};
        //string end = ")=\\)";
        
        for (int i=0; i<list.Count(); i++){
                    
                    if(i==0){
    
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\begingroup");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\LARGE "+title+" \\\\");
                        Console.WriteLine("    \\small ("+subtitle+")");
                        Console.WriteLine("\\end{center}");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        Console.WriteLine(latex[0]);
                        //Console.WriteLine("\\subsection{Exercise "+(i/30+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*), align=center,leftmargin=40pt]");
                        Console.WriteLine(latex[1]);
    
                    
                    }
                    Console.WriteLine(list[i]);
                   
                    if (i!=0 && (i+1)%30==0){
                      
                        
                        Console.WriteLine("    \\end{enumerate}");
                        Console.WriteLine("\\end{multicols}");
                        Console.WriteLine("\\end{center}");
                        Console.WriteLine();
                        Console.WriteLine("\\newpage");
                        Console.WriteLine();
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-33mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\hspace*{-10mm}\\begingroup");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\LARGE "+title+" \\\\");
                        Console.WriteLine("    \\small ("+subtitle+")");
                        Console.WriteLine("\\end{center}");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        //Console.WriteLine("\\subsection{Exercise "+((i+30)/30+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*), align=center,leftmargin=40pt]");
                        Console.WriteLine(latex[1]);
                    }
                }
        }
        
        public static void PrintArithmetic<T>(List<T> list, string title, int questions) {
        
        //string title = "Title ()";
        //string exerciseTitle = "Instructions";
        //int m=0;
        //int i_final=30000;
        //int incre= 0;
        
        string[] latex = new string[] {"\\fontsize{16pt}{25pt}\\selectfont", "        \\setlength\\itemsep{10pt}"};
        
        string[] op = new string[2] {"(", ")("};
        //string end = ")=\\)";
        
        for (int i=0; i<list.Count(); i++){
                    
                    if(i==0){
    
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\begingroup");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\end{center}");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        Console.WriteLine(latex[0]);
                        //Console.WriteLine("\\subsection{Exercise "+(i/questions+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*), align=center,leftmargin=40pt]");
                        Console.WriteLine(latex[1]);
    
                    
                    }
                    Console.WriteLine(list[i]);
                   
                    if (i!=0 && (i+1)%questions==0){
                      
                        
                        Console.WriteLine("    \\end{enumerate}");
                        Console.WriteLine("\\end{multicols}");
                        Console.WriteLine("\\end{center}");
                        Console.WriteLine();
                        Console.WriteLine("\\newpage");
                        Console.WriteLine();
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-33mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\hspace*{-10mm}\\begingroup");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\end{center}");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        //Console.WriteLine("\\subsection{Exercise "+((i+questions)/questions+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*), align=center,leftmargin=40pt]");
                        Console.WriteLine(latex[1]);
                    }
                }
        }
        
        public static void Print<T>(List<T> list, string title, string exerciseTitle) {
        
        //string title = "Title ()";
        //string exerciseTitle = "Instructions";
        //int m=0;
        //int i_final=30000;
        //int incre= 0;
        
        string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{2em}"};
        
        string[] op = new string[2] {"(", ")("};
        //string end = ")=\\)";
        
        for (int i=0; i<list.Count(); i++){
                    
                    if(i==0){
    
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\begingroup");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\end{center}");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        Console.WriteLine(latex[0]);
                        Console.WriteLine("\\subsection{Exercise "+(i/30+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
    
                    
                    }
                    Console.WriteLine(list[i]);
                   
                    if (i!=0 && (i+1)%30==0){
                      
                        
                        Console.WriteLine("    \\end{enumerate}");
                        Console.WriteLine("\\end{multicols}");
                        Console.WriteLine("\\end{center}");
                        Console.WriteLine();
                        Console.WriteLine("\\newpage");
                        Console.WriteLine();
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\begingroup");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\end{center}");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        Console.WriteLine(latex[0]);
                        Console.WriteLine("\\subsection{Exercise "+((i+30)/30+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{center}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
                    }
                }
        }
        
        public static void PrintAnswerKey<T>(List<T> list, string title, int questions) {
            
            int p = 5; // number of pages before new page
            Console.WriteLine();
            Console.WriteLine("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%");
            Console.WriteLine();
            Console.WriteLine("\\newpage");
            Console.WriteLine();
            Console.WriteLine("\\newgeometry{");
            Console.WriteLine(" a4paper,");
            Console.WriteLine(" total={170mm,257mm},");
            Console.WriteLine(" left=15mm,"); // 10mm for fractions
            Console.WriteLine(" top=20mm,");
            Console.WriteLine(" bottom=20mm,"); 
            Console.WriteLine(" right=15mm"); //10mm for fractions
            Console.WriteLine(" }");
            Console.WriteLine("\\fontsize{10pt}{10pt}\\selectfont");
            Console.WriteLine();
            Console.WriteLine("\\section{"+title+" Answer Key}");
            
            for (int i=0; i<list.Count(); i++){
                    
                if(i==0){

Console.WriteLine("\\textbf{p"+(i/questions+1)+"}");
                    Console.WriteLine();
                    Console.WriteLine("\\begin{multicols}{5}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");

}
                                      
                Console.WriteLine(list[i]);

if (i!=0 && (i+1)%(questions*p)==0){

Console.WriteLine("    \\end{enumerate}");
                    Console.WriteLine("\\end{multicols}");
                    Console.WriteLine();
                    Console.WriteLine("\\newpage");
                    Console.WriteLine();
                    Console.WriteLine("\\textbf{p"+((i+questions)/questions+1)+"}");
                    Console.WriteLine();
                    Console.WriteLine("\\begin{multicols}{5}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                }
                
                if (i!=0 && (i+1)%questions==0 && (i+1)%(questions*p)!=0){

Console.WriteLine("    \\end{enumerate}");
                    Console.WriteLine("\\end{multicols}");
                    Console.WriteLine();
                    Console.WriteLine("\\textbf{p"+((i+questions)/questions+1)+"}");
                    Console.WriteLine("\\begin{multicols}{5}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                }
                
                
            }
        }
        
        public static void Print<T>(List<T> list, string title, string exerciseTitle, int questions) {
        
            //string title = "Title ()";
            //string exerciseTitle = "Instructions";
            //int m=0;
            //int i_final=30000;
            //int incre= 0;

string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{2em}"};

string[] op = new string[2] {"(", ")("};
            //string end = ")=\\)";

for (int i=0; i<list.Count(); i++){
                    
                if(i==0){

Console.WriteLine("\\begin{figure}[ht!]");
                    Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                    Console.WriteLine("\\end{figure}");
                    Console.WriteLine();
                    Console.WriteLine("\\vspace{-15mm}\\begingroup");
                    Console.WriteLine("\\centering");
                    Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                    Console.WriteLine("\\endgroup");
                    Console.WriteLine();
                    Console.WriteLine(latex[0]);
                    Console.WriteLine("\\subsection{Exercise "+(i/questions+1)+". "+exerciseTitle+".}");
                    Console.WriteLine("\\begin{multicols}{2}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                    Console.WriteLine(latex[1]);

}
                Console.WriteLine(list[i]);

if (i!=0 && (i+1)%questions==0){

Console.WriteLine("    \\end{enumerate}");
                    Console.WriteLine("\\end{multicols}");
                    Console.WriteLine();
                    Console.WriteLine("\\newpage");
                    Console.WriteLine();
                    Console.WriteLine("\\begin{figure}[ht!]");
                    Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                    Console.WriteLine("\\end{figure}");
                    Console.WriteLine();
                    Console.WriteLine("\\vspace{-15mm}\\begingroup");
                    Console.WriteLine("\\centering");
                    Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                    Console.WriteLine("\\endgroup");
                    Console.WriteLine();
                    Console.WriteLine(latex[0]);
                    Console.WriteLine("\\subsection{Exercise "+((i+questions)/questions+1)+". "+exerciseTitle+".}");
                    Console.WriteLine("\\begin{multicols}{2}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                    Console.WriteLine(latex[1]);
                }
            }
        }
        
        public static void PrintFraction<T>(List<T> list, string title, string exerciseTitle) {
        
        //string title = "Title ()";
        //string exerciseTitle = "Instructions";
        //int m=0;
        //int i_final=30000;
        //int incre= 0;
        
        string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{1.8em}"};
        
        string[] op = new string[2] {"(", ")("};
        //string end = ")=\\)";
        
        for (int i=0; i<list.Count(); i++){
                    
                    if(i==0){
    
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\hspace*{-10mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        //Console.WriteLine(latex[0]);
                        Console.WriteLine("\\vspace{-5mm}\\subsection{Exercise "+(i/20+1)+". "+exerciseTitle+".}");
                        //Console.WriteLine("\\begin{tasks}(2)");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
    
                    
                    }
                    Console.WriteLine(list[i]);
                   
                    if (i!=0 && (i+1)%20==0){
                      
                        
                        //Console.WriteLine("\\end{tasks}");
                        Console.WriteLine("    \\end{enumerate}");
                        Console.WriteLine("\\end{multicols}");
                        Console.WriteLine();
                        Console.WriteLine("\\newpage");
                        Console.WriteLine();
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\hspace*{-10mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        //Console.WriteLine(latex[0]);
                        Console.WriteLine("\\subsection{Exercise "+((i+20)/20+1)+". "+exerciseTitle+".}");
                        //Console.WriteLine("\\begin{tasks}(2)");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
                    }
                }
        }
        
        public static long GCD(long a, long b)
        {
            return b == 0 ? a : GCD(b, a % b);
        }
        
        public static long GCD(long a, long b, long c)
        {
            return GCD(a, GCD(b,c));
        }
        
         public static void LCM(int a, int b) {

int lcm;

int a_r=a;
             int b_r=b;
             int d=max(a_r,b_r);
             
             while(d>1) {
                 
                 if (a_r%d==0 && b_r%d==0) {
                     
                     int a_r_temp=a_r/d;
                     int b_r_temp=b_r/d;
                     a_r=a_r_temp;
                     b_r=b_r_temp;
                     lcm=d*a_r*b_r;
                     break;
                     
                 }
               
                 d--;

}
             
             lcm=d*a_r*b_r;
             Console.WriteLine("LCM({0},{1}): {2}", a,b,lcm);
         }
        
        public static int lcm(int a, int b) {

int lcm;

}
             
             return d*a_r*b_r;
             //Console.WriteLine("LCM({0},{1}): {2}", a,b,lcm);
         }
             
             
            
        public static void LCM(int a, int b, int c) {
     
            Console.WriteLine("LCM("+a+","+b+","+c+"): " + lcm(a,lcm(b,c)));
        }

public static int lcm(int a, int b, int c) {
     
            return lcm(a,lcm(b,c));
            
        }
        
        public static int max(int a, int b) {
            
            if (a>b){
                return a;
            }
            else if (b>a){
                return b;
            }
            else {
                return a;
            }
        }
        
        public static int max(int a, int b, int c) {

return max(a,max(b,c));
        }

public static int min(int a, int b) {
            
            if (a>b){
                return b;
            }
            else if (b>a){
                return a;
            }
            else {
                return a;
            }
        }
        
        public static int min(int a, int b, int c) {

return min(a,min(b,c));
        }

public static void Pyth(int lowerBound, int upperBound) {
            //Your code goes here
                       
            for (int i=lowerBound; i<=upperBound; i++) {
                
                for (int j=lowerBound; j<=upperBound; j++){
                    
                    double c = Math.Sqrt(Math.Pow(i,2)+Math.Pow(j,2));
                    if (c%1==0){
                        
                        Console.WriteLine("(a,b,c) = (" + i + "," + j + "," + c + ")");
                    }
                }
            }
        }
        
        public static void areaTrapezoid(double top, double bottom, double height) {
            
            double area = (top+bottom)*height/2;
            Console.WriteLine("Area: {0}", area);
    
        }

public static void volumeCylinder ( double radius, double height) {
            
            double vol = radius*radius*Math.PI*height;
            Console.WriteLine("Volume: {0}", vol);
        
        }

public static void sAreaCylinder(double radius, double height) {
            
            double s_area = 2*calcAreaCircle(radius) + calcAreaCircle(radius)*height;
            Console.WriteLine("Surface Area: {0}", s_area);
        }

public static void Circumf(int radius){
            
            double circ = 2*radius*Math.PI;
            Console.WriteLine("Circumference: {0}", circ);
        }
                
    
        public static void areaCircle(double r){
            double area = r*r*Math.PI;
            Console.WriteLine("Area: {0}", area);
        }
        
        public static double calcAreaCircle(double r){
        
            return r*r*Math.PI;
    
        }
        
        public static double calcCircumCircle(double r){
            
            return 2*r*Math.PI;
        }
    
        public static double sAreaCone(int r, int l) {

return Math.PI*r*r+Math.PI*r*l;
		}

public static double volumeCone(int r, int h){
			
			return Math.PI*r*r/3;
		}

public static void SimplifyRatio(int ratio1, int ratio2, int ratio3) {
            
            int divisor;
            if (ratio1>ratio2 && ratio1>ratio3) {
                divisor = ratio1;
             }
            else if (ratio2>ratio1 && ratio2>ratio3) {
                divisor = ratio2;
            }
            else divisor = ratio3;

int ratio1_reduce = ratio1;
            int ratio2_reduce = ratio2;
            int ratio3_reduce = ratio3;
            while (divisor!=1) {

if(ratio1_reduce%divisor==0 && ratio2_reduce%divisor==0 && ratio3_reduce%divisor==0){
                int ratio1_reduce_temp = ratio1_reduce/divisor;
                int ratio2_reduce_temp = ratio2_reduce/divisor;
                int ratio3_reduce_temp = ratio3_reduce/divisor;

ratio1_reduce = ratio1_reduce_temp;
                ratio2_reduce = ratio2_reduce_temp;
                ratio3_reduce = ratio3_reduce_temp;
                divisor--;
            }
            else divisor--;

}
            
            Console.WriteLine(ratio1+":"+ratio2+":"+ratio3+" = "+ratio1_reduce+":"+ratio2_reduce+":"+ratio3_reduce);
        }
        
        public static void checkAlgebra(){
            
            for (int x = -40; x<40; x++) {
                
                int a = 62*x-68;
                int b = 35;
                
                if (a%b==0){
                        
                    Console.WriteLine(x);
                }
            }
            
            
        }

public static void addLineBreak(int linesPerSection, int totalLines) {
         
            for (int i=0; i<=totalLines; i++) {
                
                if (i%linesPerSection==0) {
                    
                    Console.WriteLine("Break");
                    
                }
                
                else Console.WriteLine("No");
                
            
            }
        }
                 
        public static void circleX(double x, double radius) {
            
            Console.WriteLine("("+x+", "+Math.Round(Math.Sqrt(radius*radius-Math.Pow(x,2)),3)+")");
            
        }
        
        public static void circleY(double y, double radius) {
          
            Console.WriteLine("("+y+", "+Math.Round(Math.Sqrt(radius*radius-Math.Pow(y,2)),3)+")");
            
        }
        
        public static void angle(double x1, double y1, double x2, double y2, double x3, double y3) {
         
            double l12 = Math.Pow((x1-x2),2) +Math.Pow((y1-y2),2);
            double l13 = Math.Pow((x3-x1),2) +Math.Pow((y3-y1),2);
            double l23 = Math.Pow((x3-x2),2) +Math.Pow((y3-y2),2);
            
            double lhs = (l13-l12-l23)/(-2*Math.Sqrt(l12)*Math.Sqrt(l23));
            double angle2 = Math.Acos(lhs);
            //double angle2 = Math.Round(Math.Acos()*100,3);
            
            //Console.WriteLine(angle2 + " degrees C");
            Console.WriteLine(l12 + " " + l23 + " " + l13);
            Console.WriteLine(lhs);
                Console.WriteLine(angle2*360/(2*Math.PI)+" degrees");
        }
        
        
    }
    
    public static class Rand
    { 
        /// <summary> 
        /// Random number generator used to generate seeds, 
        /// which are then used to create new random number 
        /// generators on a per-thread basis. 
        /// </summary> 
        private static readonly Random globalRandom = new Random(); 
        private static readonly object globalLock = new object();

/// <summary> 
        /// Random number generator 
        /// </summary> 
        private static readonly ThreadLocal<Random> threadRandom = new ThreadLocal<Random>(NewRandom);

/// <summary> 
        /// Creates a new instance of Random. The seed is derived 
        /// from a global (static) instance of Random, rather 
        /// than time. 
        /// </summary> 
        public static Random NewRandom() 
        { 
            lock (globalLock) 
            { 
                return new Random(globalRandom.Next()); 
            } 
        }

/// <summary> 
        /// Returns an instance of Random which can be used freely 
        /// within the current thread. 
        /// </summary> 
        public static Random Instance { get { return threadRandom.Value; } }

/// <summary>See <see cref="Random.Next()" /></summary> 
        public static int Next() 
        { 
            return Instance.Next(); 
        }

/// <summary>See <see cref="Random.Next(int)" /></summary> 
        public static int Next(int maxValue) 
        { 
            return Instance.Next(maxValue); 
        }

/// <summary>See <see cref="Random.Next(int, int)" /></summary> 
        public static int Next(int minValue, int maxValue) 
        { 
            return Instance.Next(minValue, maxValue); 
        }

public static int NextPM(int minValue, int maxValue) 
        { 
		// positive
			if (Rand.Next(0,2)==0) {
				return Instance.Next(minValue, maxValue); 
			}
			
			else
            return -Instance.Next(minValue, maxValue); 
        }
        
        /// <summary>See <see cref="Random.NextDouble()" /></summary> 
        public static double NextDouble() 
        { 
            return Instance.NextDouble(); 
        }

/// <summary>See <see cref="Random.NextBytes(byte[])" /></summary> 
        public static void NextBytes(byte[] buffer) 
        { 
            Instance.NextBytes(buffer); 
        } 
        
        public static double NextD(double minValue, double maxValue) {
            
            return Instance.NextDouble()*(maxValue-minValue)+minValue;
        }
    } 
}

namespace ShuffleExtension {
    
    public static class ShuffleExtend {
        
        //private static readonly Random rnd = new Random();
        
        public static void Shuffle<T>(this IList<T> list) {
        
            int n = list.Count; 
       
            while (n > 1) {
            
                int k = (Rextester.Rand.Next(0, n) % n);
                n--;
                T value = list[k];
                list[k] = list[n];    
                list[n] = value;
        
            }
            
        }
    }
}

namespace CountExtension {
    
    public static class CountExtension {
        
        public static int Count(this int n) {
            //return (Value == 0 ? 1 : ((int)Math.Floor(Math.Log10(Math.Abs(Value))) + 1));
            return (n == 0 ? 1 : (int)Math.Log10(Math.Abs(n)) + 1);
        
        } 
        
    }
}

namespace MathSpace {

public struct Fraction
    {
        public long num;
        public long denom;
		public long integer;
        public long Num
        {
            get
            {
                return num;
            }
            set
            {
                num = value;
            }
        }
        public long Denom
        {
            get
            {
                return denom;
            }
            set
            {
                denom = value;
            }
        }
		public long Integer
		{
			get
			{
				return integer;
			}
			set
			{
				integer = value;
			}
		}
		
        public Fraction(int num, int denom)
        {
            // num + denom - 
            if (num > 0 && denom < 0) {
                this.num = -num;
                this.denom = Math.Abs(denom);
                this.integer = 0;
            }
            // num - denom +
            else if (num < 0 && denom > 0 ) {
                this.num = -Math.Abs(num);
                this.denom = Math.Abs(denom);
                this.integer = 0;
            }
            // both positive or negative or zero
            else {
                this.num = Math.Abs(num);
                this.denom = Math.Abs(denom);
                this.integer = 0;
            }
        }
        public Fraction(long num, long denom)
        {
            // num + denom - 
            if (num > 0 && denom < 0) {
                this.num = -num;
                this.denom = Math.Abs(denom);
                this.integer = 0;
            }
            // num - denom +
            else if (num < 0 && denom > 0 ) {
                this.num = num;
                this.denom = Math.Abs(denom);
                this.integer = 0;
            }
            // both positive or negative or zero
            else {
                this.num = Math.Abs(num);
                this.denom = Math.Abs(denom);
                this.integer = 0;
            }
        }
        public Fraction(int integer, int num, int denom)
        {
            if (num*denom<0) throw new ArgumentException("Numerator and Denominator must be positive.");
            
            // all + or only two +
            if (integer * num * denom > 0 ) {
               this.integer = Math.Abs(integer);
               this.num = Math.Abs(num);
               this.denom = Math.Abs(denom); 
            }
            // if an odd -
            else {
               this.integer = -integer;
               this.num = Math.Abs(num);
               this.denom = Math.Abs(denom); 
            }
        }
        public Fraction(long integer, long num, long denom)
        {
            if (num*denom<0) throw new ArgumentException("Numerator and Denominator must be positive.");
			 // all + or only two +
            if (integer * num * denom > 0 ) {
               this.integer = Math.Abs(integer);
               this.num = Math.Abs(num);
               this.denom = Math.Abs(denom); 
            }
            // if an odd -
            else {
               this.integer = -integer;
               this.num = Math.Abs(num);
               this.denom = Math.Abs(denom); 
            }
        }
        
        public Fraction (Fraction left, int right)
        {
            Fraction result = left/right;
            this.num = result.num;
            this.denom = result.denom;
            this.integer = 0;
        }
        
        public Fraction (int left, Fraction right)
        {
            Fraction result = left/right;
            this.num = result.num;
            this.denom = result.denom;
            this.integer = 0;
        }
        
        public Fraction (Fraction left, Fraction right)
        {
            Fraction result = left/right;
            this.num = result.num;
            this.denom = result.denom;
            this.integer = 0;
        }

public Fraction toMixed()
        {
            if (this.integer == 0 && (this.num < 0 || this.denom < 0))
            {
                return new Fraction(this.num / this.denom, Math.Abs(this.num % this.denom), Math.Abs(this.denom));
            }
            else if (this.integer == 0 && (this.num * this.denom > 0))
            {
                return new Fraction(this.num / this.denom, this.num % this.denom, this.denom);
            }
            else return new Fraction(this.integer + this.num / this.denom, this.num % this.denom, this.denom);
        }
        
        public Fraction toImproper()
        {
            if (this.integer!=0 && this.integer<0) {
                return new Fraction (-(Math.Abs(this.integer)*Math.Abs(this.denom)+Math.Abs(this.num)),Math.Abs(this.denom));
            }
            
            else if (this.integer!=0 && this.integer>0) {
                return new Fraction (Math.Abs(this.integer)*Math.Abs(this.denom)+Math.Abs(this.num),Math.Abs(this.denom));
            }
            else return new Fraction (this.num,this.denom);
        }
        
        public override string ToString()
        {
            if (this.denom == 0)
            {
                return "Div by 0";
            }
            
            // if fraction is proper or improper fraction
            if (this.denom != 1 && this.integer == 0 && this.num%this.denom!=0)
            {
                // if fraction is negative (either num or denom negative but not both)
                if ((this.num < 0 || this.denom < 0 ) && !(this.num<0 && this.denom<0) )
                {
                    this.denom = Math.Abs(this.denom);
                    return this.num + "/" + this.denom;
                }
                // if fraction is positive
                else return num + "/" + denom; // + ", " + num/denom + " " + num%denom + "/" + denom;
            }
			
			//if fraction is mixed number
			else if (this.denom != 1 && this.integer != 0 && this.num%this.denom!=0)
            {
                var new_integer = Math.Abs(this.integer) + this.num/this.denom;
                var new_num = this.num % this.denom;
                this.integer = new_integer;
                this.num = new_num;
                // if fraction is negative (either num or denom negative but not both)
                if (this.integer < 0)
                {
                    return this.integer + " " + this.num + "/" + this.denom;
                }
                // if fraction is positive
                else return this.integer + " " + this.num + "/" + this.denom;
            }

// if denom not 1 and numerator is a multiple of the denominator (ie. 4/2 ==> 2) and not mixed number (result is integer)
            else if (this.num % this.denom == 0 && this.integer==0)
            {
                return (this.num / this.denom).ToString();
            }
            
			// if denom not 1 and numerator is a multiple of the denominator (ie. 4/2 ==> 2) and mixed number (result is integer)
			else if (this.num % this.denom == 0 && this.integer!=0)
            {
                return (this.integer+(this.num / this.denom)).ToString();
            }
			
            // if denominator is 1, ie., whole number and not mixed number
			
			else if (this.integer!=0) {
				return (integer+num).ToString();
			}
			
            else return num.ToString();
			
        }

public Fraction Simplify()
        {
            int divisor = Convert.ToInt32(GCD(this.num, this.denom));
            if (this.denom != 0 && this.integer==0 && this.num >0)
            {
                return new Fraction(this.num / divisor, this.denom / divisor);
            }
            
            else if (this.denom != 0 && this.integer==0 && this.num <0)
            {
                return new Fraction(-Math.Abs(this.num / divisor), Math.Abs(this.denom / divisor));
            }
            
            else if (this.denom != 0 && this.integer!=0)
            {
                 return new Fraction(this.integer, this.num / divisor, this.denom / divisor);
                
            }
                
            else return new Fraction (this.num, this.denom);

}
        public static long GCD(long a, long b)
        {
            return b == 0 ? a : GCD(b, a % b);
        }
        
        public Fraction Reciprocal()
        {
            return new Fraction(this.Denom, this.Num);
        }

public static Fraction operator +(Fraction left, Fraction right)
        {
            Fraction result;
			if (left.integer==0 &&right.integer==0){
                result = new Fraction(left.num * right.denom + right.num * left.denom, left.denom * right.denom);
                
            }
			else { 
				//result = new Fraction((left.integer*left.denom+left.num)*right.denom+(right.integer*right.denom+right.num)*left.denom, left.denom * right.denom);
				result = (new Fraction(left.integer+right.integer, left.num * right.denom + right.num * left.denom, left.denom * right.denom)).toMixed();
			}
            return result.toMixed().Simplify();
        }

public static Fraction operator +(int left, Fraction right)
        {
            Fraction result;
            if (right.integer==0) {
                result = new Fraction(left * right.denom + right.num, right.denom);
            }
            else {
                result = (new Fraction(left+right.integer, right.num, right.denom)).toMixed();
            }
            return result.Simplify();
        }

public static Fraction operator +(Fraction left, int right)
        {
            Fraction result;
            if (left.integer==0) {
                result = new Fraction(left.num + left.denom * right, left.denom);
            }
    
            else {
                result = (new Fraction(left.integer+right, left.denom)).toMixed();
            }
            return result.Simplify();
        }
        
        public static Fraction operator -(Fraction frac)
        {
            if (frac.integer==0) {
                return new Fraction(-frac.num,frac.denom);
            }
            else return (new Fraction (-frac.integer,frac.num,frac.denom)).toMixed();
                
        }

public static Fraction operator -(Fraction left, Fraction right)
        {
            Fraction result;
            if (left.integer==0 && right.integer==0) {
                result = (new Fraction(left.num * right.denom - right.num * left.denom, left.denom * right.denom)).toMixed();
            }
            
            else {
                if (((left.integer*left.denom+left.num)/left.denom)>=((right.integer*right.denom+right.num)/right.denom)) {
                    result = (left.toImproper()-right.toImproper()).toMixed();
                }
                else result = (left.toImproper()-right.toImproper()).toMixed();
            }
            return result.Simplify();
        }

public static Fraction operator -(int left, Fraction right)
        {
            Fraction result;
            if (right.integer==0) {
                result = new Fraction(left * right.denom - right.num, right.denom);
            }
            else result = (new Fraction(left * right.denom - right.toImproper().num, right.denom)).toMixed();
            
            return result.Simplify();
        }

public static Fraction operator -(Fraction left, int right)
        {
            Fraction result;
            if (left.integer==0) {
                result = new Fraction(left.num - left.denom * right, left.denom);
            }
            // if mixed numbers
            else result = (new Fraction(left.toImproper().num - left.denom * right, left.denom)).toMixed();
            
            return result.Simplify();
        }

public static Fraction operator *(Fraction left, Fraction right)
        {
            Fraction result;
            
            if (left.integer==0 && right.integer==0){
                result = new Fraction(left.num * right.num, Math.Abs(left.denom * right.denom));
            }
            // if mixed numbers
            else result = (left.toImproper()*right.toImproper()).toMixed();
                
            return result.Simplify();
        }

public static Fraction operator *(int left, Fraction right)
        {
            Fraction result;
            if (right.integer==0){
                result = new Fraction(left * right.num, right.denom);
            }
            else result = (new Fraction(right.toImproper().num * left, right.denom)).toMixed();
            
            return result.Simplify();
        }

public static Fraction operator *(Fraction left, int right)
        {
            Fraction result;
            // if improper fraction
            if (left.integer==0){
                result = new Fraction(left.num * right, left.denom);
            }
            // if mixed numbers
            else result = (new Fraction(left.toImproper().num * right, left.denom)).toMixed();
            
            return result.Simplify();
        }

public static Fraction operator /(Fraction left, Fraction right)
        {
            Fraction result;
            if (left.integer==0 &&right.integer==0){
                result = left * right.Reciprocal();
            }
            else result = (left.toImproper() * right.toImproper().Reciprocal()).toMixed();
                
            return result.Simplify();
        }

public static Fraction operator /(int left, Fraction right)
        {
            Fraction result;
            if (right.integer==0) {
                result = left * right.Reciprocal();
            }
            else result = left * right.toImproper().Reciprocal();
            
            return result.Simplify();
        }

public static Fraction operator /(Fraction left, int right)
        {
            Fraction rightRecip = new Fraction(1,right);
            Fraction result;
            if (left.integer==0) {
                result = left * rightRecip;
            }
            else {
                result = left.toImproper() * rightRecip;
            }
            return result.Simplify();
        }

public static int LCM(int a, int b)
        {
            int lcm;
            int a_r = a;
            int b_r = b;
            int d = max(a_r, b_r);

while (d > 1)
            {
                if (a_r % d == 0 && b_r % d == 0)
                {
                    int a_r_temp = a_r / d;
                    int b_r_temp = b_r / d;
                    a_r = a_r_temp;
                    b_r = b_r_temp;
                    lcm = d * a_r * b_r;
                    break;
                }
                d--;
            }
            lcm = d * a_r * b_r;
            return lcm;
        }

public static int LCM(long a, long b)
        {
            int lcm;
            long a_r = a;
            long b_r = b;
            int d = Convert.ToInt32(max(a_r, b_r));

while (d > 1)
            {
                if (a_r % d == 0 && b_r % d == 0)
                {
                    long a_r_temp = a_r / d;
                    long b_r_temp = b_r / d;
                    a_r = a_r_temp;
                    b_r = b_r_temp;
                    lcm = Convert.ToInt32(d * a_r * b_r);
                    break;
                }
                d--;
            }
            lcm = Convert.ToInt32(d * a_r * b_r);
            return lcm;
        }

public static int max(int a, int b)
        {

if (a > b)
            {
                return a;
            }
            else if (b > a)
            {
                return b;
            }
            else
            {
                return a;
            }
        }

public static long max(long a, long b)
        {

if (a > b)
            {
                return a;
            }
            else if (b > a)
            {
                return b;
            }
            else
            {
                return a;
            }
        }
		
        public double toDeci() 
        {  
            if (this.integer==0) {
                return (double) this.num/this.denom;
            }
            else {
                return (double) (this.integer*this.denom+this.num)/this.denom;
            }
        }
        
        public static Fraction toFrac(double deci)
        {
            /*List<double> d = new List<double>();
            List<double> z = new List<double>();
            List<double> n = new List<double>();*/

double[] d = new double[6];
            double[] z = new double[6];
            double[] n = new double[6];
            z[1] = deci; //X
            d[0] = 0;
            d[1] = 1;

for (int i = 1; i < 5; i++)
            {
                z[i + 1] = 1 / (z[i] - Math.Floor(z[i]));
                d[i + 1] = d[i] * Math.Floor(z[i + 1]) + d[i - 1];
                n[i + 1] = Math.Round(z[1] * d[i + 1]);
            }
            int num, denom;
            num = (int)n[5];
            denom = (int)d[5];

return new Fraction(num, denom);
        }

/*        public static Fraction RealToFraction(double value, double error)
                {
                    if (error <= 0.0 || error >= 1.0)
                    {
                        throw new ArgumentOutOfRangeException("error", "Must be between 0 and 1 (exclusive).");
                    }

int sign = Math.Sign(value);

if (sign == -1)
                    {
                        value = Math.Abs(value);
                    }

if (sign != 0)
                    {
                        // error is the maximum relative error; convert to absolute
                        error *= value;
                    }

int n = (int)Math.Floor(value);
                    value -= n;

if (value < error)
                    {
                        return new Fraction(sign * n, 1);
                    }

if (1 - error < value)
                    {
                        return new Fraction(sign * (n + 1), 1);
                    }

// The lower fraction is 0/1
                    int lower_n = 0;
                    int lower_d = 1;

// The upper fraction is 1/1
                    int upper_n = 1;
                    int upper_d = 1;

while (true)
                    {
                        // The middle fraction is (lower_n + upper_n) / (lower_d + upper_d)
                        int middle_n = lower_n + upper_n;
                        int middle_d = lower_d + upper_d;

if (middle_d * (value + error) < middle_n)
                        {
                            // real + error < middle : middle is our new upper
                            upper_n = middle_n;
                            upper_d = middle_d;
                        }
                        else if (middle_n < (value - error) * middle_d)
                        {
                            // middle < real - error : middle is our new lower
                            lower_n = middle_n;
                            lower_d = middle_d;
                        }
                        else
                        {
                            // Middle is our best fraction
                            return new Fraction((n * middle_d + middle_n) * sign, middle_d);
                        }
                    }
                }*/

public static Fraction Parse(string input)
        {
            if (String.IsNullOrWhiteSpace(input)) {
                throw new ArgumentNullException();
            }

//var instance = new Fraction();

// checks if there is more than one "/"
            if (input.IndexOf("/") != input.LastIndexOf("/")) {
                throw new ArgumentException();
            }
            //return instance;

int v;

// 
            if (input.IndexOf("/") != -1)
            {
                if (int.TryParse(input.Substring(0, input.IndexOf("/")), out v)
             && int.TryParse(input.Substring(input.IndexOf("/") + 1), out v))
                {
                    int num1 = int.Parse(input.Substring(0, input.IndexOf("/")));
                    int denom1 = int.Parse(input.Substring(input.IndexOf("/") + 1));
                    var frac = new Fraction(num1, denom1);
                    return frac;
                }
                else throw new IndexOutOfRangeException();
            }
            else // if 
            {
                if (int.TryParse(input, out v))
                {
                    return new Fraction(int.Parse(input), 1);
                }

else throw new IndexOutOfRangeException();
            }

}

public static bool TryParse(string input, out Fraction frac)
        {
            if (string.IsNullOrWhiteSpace(input))
            {
                frac = new Fraction(0, 0);
                return false;
            }

if (input.IndexOf("/") == -1 || input.IndexOf("/") != input.LastIndexOf("/"))
            {
                frac = new Fraction(0, 0);
                return false;
            }

long v;
            if (long.TryParse(input.Substring(0, input.IndexOf("/")), out v)
             && long.TryParse(input.Substring(input.IndexOf("/") + 1), out v))
            {

frac = new MathSpace.Fraction(1, 1);
                v = 1;
                return true;
            }
            else frac = new Fraction(0, 0); return false;
        }

public static Fraction ConvertFrom(object obj)
        {
            Fraction frac = new MathSpace.Fraction(0, 0);
            if (obj.GetType() == frac.GetType())
            {
                frac = (Fraction) obj;
                return frac;
            }
            else throw new NotSupportedException();
        }

public static double ConvertToDecimal(Fraction frac)
        {
            return Convert.ToDouble(frac.Num) / Convert.ToDouble(frac.Denom);
        }

public static double operator +(Fraction left, double right)
        {
            double result = ConvertToDecimal(left) + right;
            return result;
        }

public static double operator +(double left, Fraction right)
        {
            double result = left + ConvertToDecimal(right);
            return result;
        }

public static double operator -(Fraction left, double right)
        {
            double result = ConvertToDecimal(left) - right;
            return result;
        }

public static double operator -(double left, Fraction right)
        {
            double result = left - ConvertToDecimal(right);
            return result;
        }

public static double operator *(Fraction left, double right)
        {
            double result = ConvertToDecimal(left) * right;
            return result;
        }

public static double operator *(double left, Fraction right)
        {
            double result = left * ConvertToDecimal(right);
            return result;
        }

public static double operator /(Fraction left, double right)
        {
            double result = ConvertToDecimal(left) / right;
            return result;
        }

public static double operator /(double left, Fraction right)
        {
            double result = left / ConvertToDecimal(right);
            return result;
        }

public static Fraction Pow(Fraction frac, int n)
        {
            long num_new = (long) Math.Pow(frac.Num, n);
            long denom_new = (long) Math.Pow(frac.Denom, n);
            return new MathSpace.Fraction(num_new, denom_new);
        }
    }
}


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