解决24点游戏的方法

解决24点游戏的方法

一个解决古老游戏的小程序

A.第一版

这个小程序是最初的版本，计划最近增强功能以便解决数字不重复的解法。

1。 游戏的基本说明：大家应该都玩过这个游戏，就是用若干个10以内数字，通过加减乘除组合结果为24。

2。 游戏程序思路：通常用加括号的办法可以改变同一顺序的一组数字的运算先后，可是初步考虑这可是编译器级别的难题，因此我想通过

组成不同排序的数字来穷尽所有的组合，这样逻辑的计算顺序是由数字的顺序决定的，要容易的多。

3。 主要函数介绍：

A. Operation 是一个函数数组，用来存储加减乘除四则运算。

4。 不足之处：

A.还没有找出取不同数字的简单算法，各位有主意告诉我。（就是inputNumber里产生不重复数字，即不产生 2，2，3，4的组合。）

B.输出结果能否排列，或剔除相似的结果。（Forget it, it is too hard!)

C.输入数字个数改为3， 或者5等等，实际上我的程序是可以的，可是不知道那里有小虫子，还没有找到。

5. 输出的结果文件在此。 

#include <iostream>
#include <fstream>
#include <cmath>

using namespace std;

const int Number = 4;
const int OpNum = 6;
const int SignNum =4;

enum Op
{ADD=10, MIN=11, MUL=12, DIV=13, LEFT=14, RIGHT=15};

int OpCount = 0;
int NumCount = 0;

char *OpStr[OpNum]= {"Addition", "Minus", "Multiply", "Divide", "Left", "Right"};

char *OpSign[OpNum] = {"+", "-", "x", "/", "(", ")"};

int Operand[Number] = {0};

int Operator[Number*3]= {0};

void initialize();

void display(bool succeed, ofstream& f);

bool inputNumber();

bool findSolution(ofstream& f);

double Add(double , double);
double Mul(double , double);
double Min(double , double);
double Div(double , double);

double (*Operation[4])(double , double)= {Add, Min, Mul, Div};

int main()
{
int temp=0, times=0;
initialize();
ofstream f;
f.open("c://game24.txt");
while (inputNumber())
{
if (findSolution(f))
{
//display(true, f);
//temp++;
;
}
else
;
times++;
//display(false);  //in order to see clearly, omit the no solution display
}
cout<<"/nTotal "<<NumCount<<" solutions/n";
cout<<"/nAnd total number is"<<times<<endl;
f<<"/nTotal "<<NumCount<<" solutions out of "<<times<<" combinations/n";

return 0;
}

double Add(double num1, double num2)
{
return num1 + num2;
}

double Mul(double num1, double num2)
{
return num1 * num2;
}

double Min(double num1, double num2)
{
return num1 -num2;
}

double Div(double num1, double num2)
{
return num1/num2;
}

bool findSolution(ofstream& f)
{
void writeRecord(int num);

double total[1000] = {0};
int first=0, second=0, last=0, now=0;
bool result = false;

for (int i=0; i< SignNum; i++)
{
total[i] = Operation[i](Operand[0], Operand[1]);
}

for (int count = 0; count< Number-2; count++)
{
last += (count==0?0:pow(SignNum,count));
now += pow(SignNum, count+1);
second = now;
for (int first = last; first< now; first++)
{
for (int j= ADD; j<=DIV; j++) //control op
{
total[second] = Operation[j -10](total[first], Operand[count+2]);
if ((count==Number-3)&&fabs(total[second]-24)<0.01)
{
writeRecord(second);
display(true, f);
result = true;
NumCount++;
}
second++;
}
}

}
return result;
}

void writeRecord(int num)
{
int pos=num;
for (int i=1; i< Number-1; i++)
{
pos -= pow(SignNum, i);
}

for (i=Number -2; i>=0; i--)
{
Operator[i*2+1]= pos%SignNum+10; //from back to front, and 
pos = pos/SignNum;
}
}

void initialize()
{
for (int i=0; i< Number; i++)
{
Operand[i] = 1;
}
Operand[0] = 0; //this is ugly as I need to add 1 at each time,so make it zero to add 1
}

bool inputNumber()
{
int i=0;
while (true)
{
if (Operand[i]< 9)  //increase one by one number
{
Operand[i] ++;
return true;
}
else
{
if (i==Number -1)
break;
Operand[i] = 1;  //this is something like "进位"
i++;
}
}
return false;
}

void display(bool succeed, ofstream& f)
{
void addNumber();
void addParenthesis();
void displaySolution(ofstream& f);

if (succeed)
{
addNumber();
addParenthesis();
displaySolution(f);
}
else
{
cout<<"/nNo solution for these numbers:/n";
for (int i=0; i< Number; i++)
{
cout<<Operand[i]<<'/t';
}
cout<<endl;
}
}
void displaySolution(ofstream& f)
{
cout<<"/nThe solution is:/n";
for (int i =0; i< OpCount; i++)
{
if (Operator[i]< 10)
{
cout<<Operator[i];
f<<Operator[i];
}
else
{
cout<<" "<<OpSign[Operator[i] - 10]<<" ";
f<<" "<<OpSign[Operator[i] - 10]<<" ";
}
}
f<<'/n';
}

void addNumber()
{
for (int i=0; i< Number; i++)
{
Operator[i*2] = Operand[i];
}
OpCount = Number * 2 - 1;
}

void addParenthesis()
{
void insertParenthesis(int pos);

bool findLow= false, findHigh= false;

for (int i =0; i <OpCount; i++)
{
if (Operator[i]==11||Operator[i]==10)  //add, min
findLow = true;
else
{
if (Operator[i]==12||Operator[i]==13) //mul, div
{
if (findLow)       //only find add, min then findHigh is meaningful
findHigh = true;
}
}
if (findLow&&findHigh)
{
insertParenthesis(i);
findLow = false;
findHigh = false;
}
}
}

void insertParenthesis(int pos)
{
void insert(int pos, int item);
insert(pos, RIGHT);  //Sequence is important due to pos++
insert(0, LEFT);

}

void insert(int start, int item)
{
int hold1, hold2;

hold1 = Operator[start];
hold2 = Operator[start+1];

for (int i = start; i< OpCount; i++)
{
Operator[i + 1] = hold1;

hold1 = hold2; 
hold2 = Operator[i+2];

}
Operator[start] = item;
OpCount++;
}

A glimpse of the output in screen. Click to maximize and here is the total outcome file again.

8 x 3 + 1 - 1
8 x 3 - 1 + 1
8 x 3 x 1 x 1
8 x 3 x 1 / 1
8 x 3 / 1 x 1
8 x 3 / 1 / 1
6 x 4 + 1 - 1
6 x 4 - 1 + 1
6 x 4 x 1 x 1
6 x 4 x 1 / 1
6 x 4 / 1 x 1
6 x 4 / 1 / 1
( 5 x 5 - 1 ) x 1
( 5 x 5 - 1 ) / 1
5 x 5 x 1 - 1
5 x 5 / 1 - 1
4 x 6 + 1 - 1
4 x 6 - 1 + 1
4 x 6 x 1 x 1
4 x 6 x 1 / 1
4 x 6 / 1 x 1
4 x 6 / 1 / 1
3 x 8 + 1 - 1
3 x 8 - 1 + 1
3 x 8 x 1 x 1
3 x 8 x 1 / 1
3 x 8 / 1 x 1
3 x 8 / 1 / 1
6 x 2 x 2 x 1
6 x 2 x 2 / 1
4 x 3 x 2 x 1
4 x 3 x 2 / 1
7 x 3 + 2 + 1
( 9 + 3 ) x 2 x 1
( 9 + 3 ) x 2 / 1
9 x 3 - 2 - 1
3 x 4 x 2 x 1
3 x 4 x 2 / 1
( 8 + 4 ) x 2 x 1
( 8 + 4 ) x 2 / 1
5 x 5 - 2 + 1
( 7 + 5 ) x 2 x 1
( 7 + 5 ) x 2 / 1
2 x 6 x 2 x 1
2 x 6 x 2 / 1
( 6 + 6 ) x 2 x 1
( 6 + 6 ) x 2 / 1
8 x 6 / 2 x 1
8 x 6 / 2 / 1
3 x 7 + 2 + 1
( 5 + 7 ) x 2 x 1
( 5 + 7 ) x 2 / 1
( 4 + 8 ) x 2 x 1
( 4 + 8 ) x 2 / 1
6 x 8 / 2 x 1
6 x 8 / 2 / 1
( 3 + 9 ) x 2 x 1
( 3 + 9 ) x 2 / 1
3 x 9 - 2 - 1
( 7 + 1 ) x 3 x 1
( 7 + 1 ) x 3 / 1
8 x 1 x 3 x 1
8 x 1 x 3 / 1
8 / 1 x 3 x 1
8 / 1 x 3 / 1
( 9 - 1 ) x 3 x 1
( 9 - 1 ) x 3 / 1
4 x 2 x 3 x 1
4 x 2 x 3 / 1
( 6 + 2 ) x 3 x 1
( 6 + 2 ) x 3 / 1
( 5 + 3 ) x 3 x 1
( 5 + 3 ) x 3 / 1
( 7 x 3 + 3 ) x 1
( 7 x 3 + 3 ) / 1
( 9 x 3 - 3 ) x 1
( 9 x 3 - 3 ) / 1
2 x 4 x 3 x 1
2 x 4 x 3 / 1
( 4 + 4 ) x 3 x 1
( 4 + 4 ) x 3 / 1
5 x 4 + 3 + 1
7 x 4 - 3 - 1
( 3 + 5 ) x 3 x 1
( 3 + 5 ) x 3 / 1
4 x 5 + 3 + 1
( 2 + 6 ) x 3 x 1
( 2 + 6 ) x 3 / 1
( 1 + 7 ) x 3 x 1
( 1 + 7 ) x 3 / 1
( 3 x 7 + 3 ) x 1
( 3 x 7 + 3 ) / 1
4 x 7 - 3 - 1
1 x 8 x 3 x 1
1 x 8 x 3 / 1
9 x 8 / 3 x 1
9 x 8 / 3 / 1
( 3 x 9 - 3 ) x 1
( 3 x 9 - 3 ) / 1
8 x 9 / 3 x 1
8 x 9 / 3 / 1
( 5 + 1 ) x 4 x 1
( 5 + 1 ) x 4 / 1
6 x 1 x 4 x 1
6 x 1 x 4 / 1
6 / 1 x 4 x 1
6 / 1 x 4 / 1
( 7 - 1 ) x 4 x 1
( 7 - 1 ) x 4 / 1
3 x 2 x 4 x 1
3 x 2 x 4 / 1
( 4 + 2 ) x 4 x 1
( 4 + 2 ) x 4 / 1
( 8 - 2 ) x 4 x 1
( 8 - 2 ) x 4 / 1
2 x 3 x 4 x 1
2 x 3 x 4 / 1
( 3 + 3 ) x 4 x 1
( 3 + 3 ) x 4 / 1
7 x 3 + 4 - 1
( 9 - 3 ) x 4 x 1
( 9 - 3 ) x 4 / 1
9 x 3 - 4 + 1
( 2 + 4 ) x 4 x 1
( 2 + 4 ) x 4 / 1
( 5 x 4 + 4 ) x 1
( 5 x 4 + 4 ) / 1
( 7 x 4 - 4 ) x 1
( 7 x 4 - 4 ) / 1
( 1 + 5 ) x 4 x 1
( 1 + 5 ) x 4 / 1
( 4 x 5 + 4 ) x 1
( 4 x 5 + 4 ) / 1
1 x 6 x 4 x 1
1 x 6 x 4 / 1
3 x 7 + 4 - 1
( 4 x 7 - 4 ) x 1
( 4 x 7 - 4 ) / 1
3 x 9 - 4 + 1
( 4 + 1 ) x 5 - 1
5 x 1 x 5 - 1
5 / 1 x 5 - 1
( 6 - 1 ) x 5 - 1
( 3 + 2 ) x 5 - 1
( 7 - 2 ) x 5 - 1
9 x 2 + 5 + 1
( 2 + 3 ) x 5 - 1
6 x 3 + 5 + 1
( 8 - 3 ) x 5 - 1
( 1 + 4 ) x 5 - 1
5 x 4 + 5 - 1
7 x 4 - 5 + 1
( 9 - 4 ) x 5 - 1
1 x 5 x 5 - 1
4 x 5 + 5 - 1
6 x 5 - 5 - 1
3 x 6 + 5 + 1
5 x 6 - 5 - 1
4 x 7 - 5 + 1
2 x 9 + 5 + 1
9 + 9 + 5 + 1
( 3 + 1 ) x 6 x 1
( 3 + 1 ) x 6 / 1
4 x 1 x 6 x 1
4 x 1 x 6 / 1
4 / 1 x 6 x 1
4 / 1 x 6 / 1
( 5 - 1 ) x 6 x 1
( 5 - 1 ) x 6 / 1
( 2 + 2 ) x 6 x 1
( 2 + 2 ) x 6 / 1
2 x 2 x 6 x 1
2 x 2 x 6 / 1
( 6 - 2 ) x 6 x 1
( 6 - 2 ) x 6 / 1
8 / 2 x 6 x 1
8 / 2 x 6 / 1
( 9 x 2 + 6 ) x 1
( 9 x 2 + 6 ) / 1
( 1 + 3 ) x 6 x 1
( 1 + 3 ) x 6 / 1
( 6 x 3 + 6 ) x 1
( 6 x 3 + 6 ) / 1
( 7 - 3 ) x 6 x 1
( 7 - 3 ) x 6 / 1
1 x 4 x 6 x 1
1 x 4 x 6 / 1
( 8 - 4 ) x 6 x 1
( 8 - 4 ) x 6 / 1
( 6 x 5 - 6 ) x 1
( 6 x 5 - 6 ) / 1
( 9 - 5 ) x 6 x 1
( 9 - 5 ) x 6 / 1
( 3 x 6 + 6 ) x 1
( 3 x 6 + 6 ) / 1
( 5 x 6 - 6 ) x 1
( 5 x 6 - 6 ) / 1
9 + 8 + 6 + 1
( 2 x 9 + 6 ) x 1
( 2 x 9 + 6 ) / 1
8 + 9 + 6 + 1
( 9 + 9 + 6 ) x 1
( 9 + 9 + 6 ) / 1
8 x 2 + 7 + 1
9 x 2 + 7 - 1
6 x 3 + 7 - 1
4 x 4 + 7 + 1
8 x 4 - 7 - 1
6 x 5 - 7 + 1
3 x 6 + 7 - 1
5 x 6 - 7 + 1
9 + 7 + 7 + 1
2 x 8 + 7 + 1
4 x 8 - 7 - 1
8 + 8 + 7 + 1
( 9 + 8 + 7 ) x 1
( 9 + 8 + 7 ) / 1
2 x 9 + 7 - 1
7 + 9 + 7 + 1
( 8 + 9 + 7 ) x 1
( 8 + 9 + 7 ) / 1
9 + 9 + 7 - 1
( 2 + 1 ) x 8 x 1
( 2 + 1 ) x 8 / 1
3 x 1 x 8 x 1
3 x 1 x 8 / 1
3 / 1 x 8 x 1
3 / 1 x 8 / 1
( 4 - 1 ) x 8 x 1
( 4 - 1 ) x 8 / 1
( 1 + 2 ) x 8 x 1
( 1 + 2 ) x 8 / 1
( 5 - 2 ) x 8 x 1
( 5 - 2 ) x 8 / 1
6 / 2 x 8 x 1
6 / 2 x 8 / 1
( 8 x 2 + 8 ) x 1
( 8 x 2 + 8 ) / 1
1 x 3 x 8 x 1
1 x 3 x 8 / 1
5 x 3 + 8 + 1
( 6 - 3 ) x 8 x 1
( 6 - 3 ) x 8 / 1
9 / 3 x 8 x 1
9 / 3 x 8 / 1
( 4 x 4 + 8 ) x 1
( 4 x 4 + 8 ) / 1
( 7 - 4 ) x 8 x 1
( 7 - 4 ) x 8 / 1
( 8 x 4 - 8 ) x 1
( 8 x 4 - 8 ) / 1
3 x 5 + 8 + 1
( 8 - 5 ) x 8 x 1
( 8 - 5 ) x 8 / 1
9 + 6 + 8 + 1
( 9 - 6 ) x 8 x 1
( 9 - 6 ) x 8 / 1
8 + 7 + 8 + 1
( 9 + 7 + 8 ) x 1
( 9 + 7 + 8 ) / 1
( 2 x 8 + 8 ) x 1
( 2 x 8 + 8 ) / 1
( 4 x 8 - 8 ) x 1
( 4 x 8 - 8 ) / 1
7 + 8 + 8 + 1
( 8 + 8 + 8 ) x 1
( 8 + 8 + 8 ) / 1
9 + 8 + 8 - 1
6 + 9 + 8 + 1
( 7 + 9 + 8 ) x 1
( 7 + 9 + 8 ) / 1
8 + 9 + 8 - 1
7 x 2 + 9 + 1
8 x 2 + 9 - 1
( 5 x 3 + 9 ) x 1
( 5 x 3 + 9 ) / 1
8 / 3 x 9 x 1
8 / 3 x 9 / 1
4 x 4 + 9 - 1
8 x 4 - 9 + 1
( 3 x 5 + 9 ) x 1
( 3 x 5 + 9 ) / 1
9 + 5 + 9 + 1
8 + 6 + 9 + 1
( 9 + 6 + 9 ) x 1
( 9 + 6 + 9 ) / 1
2 x 7 + 9 + 1
7 + 7 + 9 + 1
( 8 + 7 + 9 ) x 1
( 8 + 7 + 9 ) / 1
9 + 7 + 9 - 1
2 x 8 + 9 - 1
4 x 8 - 9 + 1
6 + 8 + 9 + 1
( 7 + 8 + 9 ) x 1
( 7 + 8 + 9 ) / 1
8 + 8 + 9 - 1
5 + 9 + 9 + 1
( 6 + 9 + 9 ) x 1
( 6 + 9 + 9 ) / 1
7 + 9 + 9 - 1
6 x 2 x 1 x 2
6 x 2 / 1 x 2
( 9 + 2 + 1 ) x 2
4 x 3 x 1 x 2
4 x 3 / 1 x 2
7 x 3 + 1 + 2
( 8 + 3 + 1 ) x 2
( 9 + 3 ) x 1 x 2
( 9 + 3 ) / 1 x 2
9 x 3 - 1 - 2
3 x 4 x 1 x 2
3 x 4 / 1 x 2
( 7 + 4 + 1 ) x 2
( 8 + 4 ) x 1 x 2
( 8 + 4 ) / 1 x 2
( 9 + 4 - 1 ) x 2
5 x 5 + 1 - 2
( 6 + 5 + 1 ) x 2
( 7 + 5 ) x 1 x 2
( 7 + 5 ) / 1 x 2
( 8 + 5 - 1 ) x 2
2 x 6 x 1 x 2
2 x 6 / 1 x 2
( 5 + 6 + 1 ) x 2
( 6 + 6 ) x 1 x 2
( 6 + 6 ) / 1 x 2
( 7 + 6 - 1 ) x 2
8 x 6 x 1 / 2
8 x 6 / 1 / 2
3 x 7 + 1 + 2
( 4 + 7 + 1 ) x 2
( 5 + 7 ) x 1 x 2
( 5 + 7 ) / 1 x 2
( 6 + 7 - 1 ) x 2
( 7 x 7 - 1 ) / 2
( 3 + 8 + 1 ) x 2
( 4 + 8 ) x 1 x 2
( 4 + 8 ) / 1 x 2
( 5 + 8 - 1 ) x 2
6 x 8 x 1 / 2
6 x 8 / 1 / 2
( 2 + 9 + 1 ) x 2
( 3 + 9 ) x 1 x 2
( 3 + 9 ) / 1 x 2
3 x 9 - 1 - 2
( 4 + 9 - 1 ) x 2
( 5 + 1 ) x 2 x 2
6 x 1 x 2 x 2
6 / 1 x 2 x 2
( 7 - 1 ) x 2 x 2
( 9 + 1 + 2 ) x 2
3 x 2 x 2 x 2
( 4 + 2 ) x 2 x 2
( 5 x 2 + 2 ) x 2
( 7 x 2 - 2 ) x 2
( 8 + 2 + 2 ) x 2
( 8 - 2 ) x 2 x 2
( 9 + 2 ) x 2 + 2
2 x 3 x 2 x 2
( 3 + 3 ) x 2 x 2
( 7 + 3 + 2 ) x 2
( 8 + 3 ) x 2 + 2
8 x 3 + 2 - 2
8 x 3 - 2 + 2
8 x 3 x 2 / 2
8 x 3 / 2 x 2
( 9 - 3 ) x 2 x 2
( 2 + 4 ) x 2 x 2
5 x 4 + 2 + 2
( 6 + 4 + 2 ) x 2
6 x 4 + 2 - 2
6 x 4 - 2 + 2
6 x 4 x 2 / 2
6 x 4 / 2 x 2
( 7 + 4 ) x 2 + 2
7 x 4 - 2 - 2
( 9 + 4 ) x 2 - 2
( 1 + 5 ) x 2 x 2
( 2 x 5 + 2 ) x 2
4 x 5 + 2 + 2
( 5 + 5 + 2 ) x 2
( 6 + 5 ) x 2 + 2
( 8 + 5 ) x 2 - 2
( 9 + 5 - 2 ) x 2
1 x 6 x 2 x 2
( 4 + 6 + 2 ) x 2
4 x 6 + 2 - 2
4 x 6 - 2 + 2
4 x 6 x 2 / 2
4 x 6 / 2 x 2
( 5 + 6 ) x 2 + 2
( 7 + 6 ) x 2 - 2
( 8 + 6 - 2 ) x 2
( 2 x 7 - 2 ) x 2
( 3 + 7 + 2 ) x 2
( 4 + 7 ) x 2 + 2
4 x 7 - 2 - 2
( 6 + 7 ) x 2 - 2
( 7 + 7 - 2 ) x 2
( 2 + 8 + 2 ) x 2
( 3 + 8 ) x 2 + 2
3 x 8 + 2 - 2
3 x 8 - 2 + 2
3 x 8 x 2 / 2
3 x 8 / 2 x 2
( 5 + 8 ) x 2 - 2
( 6 + 8 - 2 ) x 2
( 1 + 9 + 2 ) x 2
( 2 + 9 ) x 2 + 2
( 4 + 9 ) x 2 - 2
( 5 + 9 - 2 ) x 2
( 3 + 1 ) x 3 x 2
4 x 1 x 3 x 2
4 / 1 x 3 x 2
( 5 - 1 ) x 3 x 2
( 8 + 1 + 3 ) x 2
( 9 x 1 + 3 ) x 2
( 9 / 1 + 3 ) x 2
( 2 + 2 ) x 3 x 2
2 x 2 x 3 x 2
( 6 - 2 ) x 3 x 2
( 7 + 2 + 3 ) x 2
8 x 2 x 3 / 2
8 / 2 x 3 x 2
( 1 + 3 ) x 3 x 2
( 3 x 3 + 3 ) x 2
( 5 x 3 - 3 ) x 2
( 6 + 3 + 3 ) x 2
( 7 - 3 ) x 3 x 2
1 x 4 x 3 x 2
4 x 4 x 3 / 2
( 5 + 4 + 3 ) x 2
( 8 - 4 ) x 3 x 2
9 x 4 / 3 x 2
( 3 x 5 - 3 ) x 2
( 4 + 5 + 3 ) x 2
5 x 5 - 3 + 2
( 9 - 5 ) x 3 x 2
( 9 x 5 + 3 ) / 2
( 3 + 6 + 3 ) x 2
6 x 6 / 3 x 2
( 9 + 6 - 3 ) x 2
( 2 + 7 + 3 ) x 2
( 8 + 7 - 3 ) x 2
( 9 + 7 ) x 3 / 2
( 1 + 8 + 3 ) x 2
2 x 8 x 3 / 2
( 7 + 8 - 3 ) x 2
( 8 + 8 ) x 3 / 2
( 1 x 9 + 3 ) x 2
4 x 9 / 3 x 2
( 5 x 9 + 3 ) / 2
( 6 + 9 - 3 ) x 2
( 7 + 9 ) x 3 / 2
( 2 + 1 ) x 4 x 2
3 x 1 x 4 x 2
3 / 1 x 4 x 2
( 4 - 1 ) x 4 x 2
( 7 + 1 + 4 ) x 2
( 8 x 1 + 4 ) x 2
( 8 / 1 + 4 ) x 2
( 9 - 1 + 4 ) x 2
( 1 + 2 ) x 4 x 2
( 4 x 2 + 4 ) x 2
( 5 - 2 ) x 4 x 2
( 6 + 2 + 4 ) x 2
6 x 2 x 4 / 2
6 / 2 x 4 x 2
( 8 x 2 - 4 ) x 2
9 x 2 + 4 + 2
1 x 3 x 4 x 2
4 x 3 x 4 / 2
( 5 + 3 + 4 ) x 2
( 6 - 3 ) x 4 x 2
6 x 3 + 4 + 2
( 9 + 3 ) x 4 / 2
9 / 3 x 4 x 2
( 2 x 4 + 4 ) x 2
3 x 4 x 4 / 2
( 4 + 4 + 4 ) x 2
( 4 x 4 - 4 ) x 2
( 7 - 4 ) x 4 x 2
( 8 + 4 ) x 4 / 2
( 3 + 5 + 4 ) x 2
6 x 5 - 4 - 2
( 7 + 5 ) x 4 / 2
( 8 - 5 ) x 4 x 2
( 2 + 6 + 4 ) x 2
2 x 6 x 4 / 2
3 x 6 + 4 + 2
5 x 6 - 4 - 2
( 6 + 6 ) x 4 / 2
8 x 6 / 4 x 2
( 9 - 6 ) x 4 x 2
( 1 + 7 + 4 ) x 2
( 5 + 7 ) x 4 / 2
( 9 + 7 - 4 ) x 2
( 1 x 8 + 4 ) x 2
( 2 x 8 - 4 ) x 2
( 4 + 8 ) x 4 / 2
6 x 8 / 4 x 2
( 8 + 8 - 4 ) x 2
2 x 9 + 4 + 2
( 3 + 9 ) x 4 / 2
( 7 + 9 - 4 ) x 2
9 + 9 + 4 + 2
( 6 + 1 + 5 ) x 2
( 7 x 1 + 5 ) x 2
( 7 / 1 + 5 ) x 2
( 8 - 1 + 5 ) x 2
( 5 + 2 + 5 ) x 2
( 9 - 2 + 5 ) x 2
( 4 + 3 + 5 ) x 2
7 x 3 + 5 - 2
9 x 3 - 5 + 2
( 3 + 4 + 5 ) x 2
( 2 + 5 + 5 ) x 2
( 1 + 6 + 5 ) x 2
( 1 x 7 + 5 ) x 2
3 x 7 + 5 - 2
9 + 8 + 5 + 2
( 9 + 8 - 5 ) x 2
3 x 9 - 5 + 2
8 + 9 + 5 + 2
( 8 + 9 - 5 ) x 2
( 1 + 1 ) x 6 x 2
2 x 1 x 6 x 2
2 / 1 x 6 x 2
( 3 - 1 ) x 6 x 2
( 5 + 1 + 6 ) x 2
( 6 x 1 + 6 ) x 2
( 6 / 1 + 6 ) x 2
( 7 + 1 ) x 6 / 2
( 7 - 1 + 6 ) x 2
8 x 1 x 6 / 2
8 / 1 x 6 / 2
( 9 - 1 ) x 6 / 2
1 x 2 x 6 x 2
( 3 x 2 + 6 ) x 2
( 4 + 2 + 6 ) x 2
( 4 - 2 ) x 6 x 2
4 x 2 x 6 / 2
4 / 2 x 6 x 2
( 6 + 2 ) x 6 / 2
( 8 - 2 + 6 ) x 2
8 x 2 + 6 + 2
( 9 x 2 - 6 ) x 2
( 2 x 3 + 6 ) x 2
( 3 + 3 + 6 ) x 2
( 5 + 3 ) x 6 / 2
( 5 - 3 ) x 6 x 2
( 6 x 3 - 6 ) x 2
6 / 3 x 6 x 2
( 9 - 3 + 6 ) x 2
( 2 + 4 + 6 ) x 2
2 x 4 x 6 / 2
( 4 + 4 ) x 6 / 2
4 x 4 + 6 + 2
5 x 4 + 6 - 2
( 6 - 4 ) x 6 x 2
7 x 4 - 6 + 2
8 x 4 - 6 - 2
8 / 4 x 6 x 2
( 1 + 5 + 6 ) x 2
( 3 + 5 ) x 6 / 2
4 x 5 + 6 - 2
( 7 - 5 ) x 6 x 2
( 1 x 6 + 6 ) x 2
( 2 + 6 ) x 6 / 2
( 3 x 6 - 6 ) x 2
( 7 x 6 + 6 ) / 2
( 8 - 6 ) x 6 x 2
( 9 x 6 - 6 ) / 2
( 1 + 7 ) x 6 / 2
4 x 7 - 6 + 2
( 6 x 7 + 6 ) / 2
9 + 7 + 6 + 2
( 9 - 7 ) x 6 x 2
1 x 8 x 6 / 2
2 x 8 + 6 + 2
4 x 8 - 6 - 2
8 + 8 + 6 + 2
9 x 8 / 6 x 2
( 2 x 9 - 6 ) x 2
( 6 x 9 - 6 ) / 2
7 + 9 + 6 + 2
8 x 9 / 6 x 2
( 9 + 9 - 6 ) x 2
( 4 + 1 + 7 ) x 2
( 5 x 1 + 7 ) x 2
( 5 / 1 + 7 ) x 2
( 6 - 1 + 7 ) x 2
( 3 + 2 + 7 ) x 2
( 7 - 2 + 7 ) x 2
( 2 + 3 + 7 ) x 2
5 x 3 + 7 + 2
( 8 - 3 + 7 ) x 2
( 1 + 4 + 7 ) x 2
( 9 - 4 + 7 ) x 2
( 1 x 5 + 7 ) x 2
3 x 5 + 7 + 2
9 + 6 + 7 + 2
8 + 7 + 7 + 2
7 + 8 + 7 + 2
6 + 9 + 7 + 2
( 3 + 1 + 8 ) x 2
( 4 x 1 + 8 ) x 2
( 4 / 1 + 8 ) x 2
( 5 + 1 ) x 8 / 2
( 5 - 1 + 8 ) x 2
6 x 1 x 8 / 2
6 / 1 x 8 / 2
( 7 - 1 ) x 8 / 2
( 2 + 2 + 8 ) x 2
( 2 x 2 + 8 ) x 2
3 x 2 x 8 / 2
3 / 2 x 8 x 2
( 4 + 2 ) x 8 / 2
( 6 - 2 + 8 ) x 2
7 x 2 + 8 + 2
( 8 - 2 ) x 8 / 2
( 8 / 2 + 8 ) x 2
9 x 2 + 8 - 2
( 1 + 3 + 8 ) x 2
2 x 3 x 8 / 2
( 3 + 3 ) x 8 / 2
6 x 3 + 8 - 2
( 7 - 3 + 8 ) x 2
( 9 - 3 ) x 8 / 2
( 1 x 4 + 8 ) x 2
( 2 + 4 ) x 8 / 2
( 5 x 4 - 8 ) x 2
6 / 4 x 8 x 2
( 8 - 4 + 8 ) x 2
( 1 + 5 ) x 8 / 2
( 4 x 5 - 8 ) x 2
6 x 5 - 8 + 2
( 8 x 5 + 8 ) / 2
9 + 5 + 8 + 2
( 9 - 5 + 8 ) x 2
1 x 6 x 8 / 2
3 x 6 + 8 - 2
5 x 6 - 8 + 2
8 + 6 + 8 + 2
9 / 6 x 8 x 2
2 x 7 + 8 + 2
7 + 7 + 8 + 2
( 8 x 7 - 8 ) / 2
( 5 x 8 + 8 ) / 2
6 + 8 + 8 + 2
( 7 x 8 - 8 ) / 2
2 x 9 + 8 - 2
5 + 9 + 8 + 2
9 + 9 + 8 - 2
( 2 + 1 + 9 ) x 2
( 3 x 1 + 9 ) x 2
( 3 / 1 + 9 ) x 2
( 4 - 1 + 9 ) x 2
( 1 + 2 + 9 ) x 2
( 5 - 2 + 9 ) x 2
( 6 / 2 + 9 ) x 2
( 1 x 3 + 9 ) x 2
4 / 3 x 9 x 2
( 6 - 3 + 9 ) x 2
( 7 x 3 - 9 ) x 2
( 9 / 3 + 9 ) x 2
( 7 - 4 + 9 ) x 2
9 + 4 + 9 + 2
7 x 5 - 9 - 2
8 + 5 + 9 + 2
( 8 - 5 + 9 ) x 2
7 + 6 + 9 + 2
8 / 6 x 9 x 2
( 9 - 6 + 9 ) x 2
( 3 x 7 - 9 ) x 2
5 x 7 - 9 - 2
6 + 7 + 9 + 2
5 + 8 + 9 + 2
9 + 8 + 9 - 2
4 + 9 + 9 + 2
8 + 9 + 9 - 2
( 6 + 1 + 1 ) x 3
( 7 + 1 ) x 1 x 3
( 7 + 1 ) / 1 x 3
( 7 x 1 + 1 ) x 3
( 7 / 1 + 1 ) x 3
( 8 + 1 - 1 ) x 3
( 8 - 1 + 1 ) x 3
8 x 1 x 1 x 3
8 x 1 / 1 x 3
8 / 1 x 1 x 3
8 / 1 / 1 x 3
( 9 - 1 ) x 1 x 3
( 9 - 1 ) / 1 x 3
( 9 x 1 - 1 ) x 3
( 9 / 1 - 1 ) x 3
4 x 2 x 1 x 3
4 x 2 / 1 x 3
( 5 + 2 + 1 ) x 3
( 6 + 2 ) x 1 x 3
( 6 + 2 ) / 1 x 3
( 7 + 2 - 1 ) x 3
( 9 - 2 + 1 ) x 3
( 3 x 3 - 1 ) x 3
( 4 + 3 + 1 ) x 3
( 5 + 3 ) x 1 x 3
( 5 + 3 ) / 1 x 3
( 6 + 3 - 1 ) x 3
7 x 3 x 1 + 3
7 x 3 / 1 + 3
9 x 3 x 1 - 3
9 x 3 / 1 - 3
2 x 4 x 1 x 3
2 x 4 / 1 x 3
( 3 + 4 + 1 ) x 3
( 4 + 4 ) x 1 x 3
( 4 + 4 ) / 1 x 3
( 5 + 4 - 1 ) x 3
5 x 4 + 1 + 3
7 x 4 - 1 - 3
( 2 + 5 + 1 ) x 3
( 3 + 5 ) x 1 x 3
( 3 + 5 ) / 1 x 3
( 4 + 5 - 1 ) x 3
4 x 5 + 1 + 3
( 1 + 6 + 1 ) x 3
( 2 + 6 ) x 1 x 3
( 2 + 6 ) / 1 x 3
( 3 + 6 - 1 ) x 3
( 1 + 7 ) x 1 x 3
( 1 + 7 ) / 1 x 3
( 1 x 7 + 1 ) x 3
( 2 + 7 - 1 ) x 3
3 x 7 x 1 + 3
3 x 7 / 1 + 3
4 x 7 - 1 - 3
( 1 + 8 - 1 ) x 3
1 x 8 x 1 x 3
1 x 8 / 1 x 3
9 x 8 x 1 / 3
9 x 8 / 1 / 3
( 1 x 9 - 1 ) x 3
3 x 9 x 1 - 3
3 x 9 / 1 - 3
8 x 9 x 1 / 3
8 x 9 / 1 / 3
( 3 + 1 ) x 2 x 3
4 x 1 x 2 x 3
4 / 1 x 2 x 3
( 5 + 1 + 2 ) x 3
( 5 - 1 ) x 2 x 3
( 6 x 1 + 2 ) x 3
( 6 / 1 + 2 ) x 3
( 7 - 1 + 2 ) x 3
( 9 + 1 - 2 ) x 3
( 2 + 2 ) x 2 x 3
2 x 2 x 2 x 3
( 3 x 2 + 2 ) x 3
( 4 + 2 + 2 ) x 3
( 5 x 2 - 2 ) x 3
( 6 - 2 ) x 2 x 3
( 8 + 2 - 2 ) x 3
( 8 - 2 + 2 ) x 3
8 x 2 / 2 x 3
8 / 2 x 2 x 3
( 1 + 3 ) x 2 x 3
( 2 x 3 + 2 ) x 3
( 3 + 3 + 2 ) x 3
( 7 + 3 - 2 ) x 3
( 7 - 3 ) x 2 x 3
( 9 - 3 + 2 ) x 3
1 x 4 x 2 x 3
( 2 + 4 + 2 ) x 3
4 x 4 / 2 x 3
( 6 + 4 - 2 ) x 3
( 8 - 4 ) x 2 x 3
9 x 4 x 2 / 3
( 1 + 5 + 2 ) x 3
( 2 x 5 - 2 ) x 3
( 5 + 5 - 2 ) x 3
5 x 5 + 2 - 3
( 9 - 5 ) x 2 x 3
( 1 x 6 + 2 ) x 3
( 4 + 6 - 2 ) x 3
6 x 6 x 2 / 3
7 x 6 / 2 + 3
9 x 6 / 2 - 3
( 3 + 7 - 2 ) x 3
6 x 7 / 2 + 3
( 9 + 7 ) / 2 x 3
( 2 + 8 - 2 ) x 3
2 x 8 / 2 x 3
( 8 + 8 ) / 2 x 3
( 1 + 9 - 2 ) x 3
4 x 9 x 2 / 3
6 x 9 / 2 - 3
( 7 + 9 ) / 2 x 3
( 4 + 1 + 3 ) x 3
( 5 x 1 + 3 ) x 3
( 5 / 1 + 3 ) x 3
( 6 + 1 ) x 3 + 3
( 6 - 1 + 3 ) x 3
7 x 1 x 3 + 3
7 / 1 x 3 + 3
( 8 + 1 ) x 3 - 3
( 8 - 1 ) x 3 + 3
9 x 1 x 3 - 3
9 / 1 x 3 - 3
( 3 + 2 + 3 ) x 3
( 5 + 2 ) x 3 + 3
( 7 + 2 ) x 3 - 3
( 7 - 2 + 3 ) x 3
( 9 + 2 - 3 ) x 3
( 9 - 2 ) x 3 + 3
9 x 2 + 3 + 3
( 2 + 3 + 3 ) x 3
3 x 3 x 3 - 3
( 4 + 3 ) x 3 + 3
( 6 + 3 ) x 3 - 3
6 x 3 + 3 + 3
( 8 + 3 - 3 ) x 3
( 8 - 3 + 3 ) x 3
8 x 3 + 3 - 3
8 x 3 - 3 + 3
8 x 3 x 3 / 3
8 x 3 / 3 x 3
8 / 3 x 3 x 3
( 1 + 4 + 3 ) x 3
( 3 + 4 ) x 3 + 3
( 5 + 4 ) x 3 - 3
6 x 4 + 3 - 3
6 x 4 - 3 + 3
6 x 4 x 3 / 3
6 x 4 / 3 x 3
( 7 + 4 - 3 ) x 3
( 9 - 4 + 3 ) x 3
( 1 x 5 + 3 ) x 3
( 2 + 5 ) x 3 + 3
( 4 + 5 ) x 3 - 3
( 6 + 5 - 3 ) x 3
6 x 5 - 3 - 3
( 1 + 6 ) x 3 + 3
( 3 + 6 ) x 3 - 3
3 x 6 + 3 + 3
4 x 6 + 3 - 3
4 x 6 - 3 + 3
4 x 6 x 3 / 3
4 x 6 / 3 x 3
( 5 + 6 - 3 ) x 3
5 x 6 - 3 - 3
1 x 7 x 3 + 3
( 2 + 7 ) x 3 - 3
( 4 + 7 - 3 ) x 3
9 x 7 / 3 + 3
( 1 + 8 ) x 3 - 3
( 3 + 8 - 3 ) x 3
3 x 8 + 3 - 3
3 x 8 - 3 + 3
3 x 8 x 3 / 3
3 x 8 / 3 x 3
1 x 9 x 3 - 3
( 2 + 9 - 3 ) x 3
2 x 9 + 3 + 3
7 x 9 / 3 + 3
9 + 9 + 3 + 3
9 x 9 / 3 - 3
( 1 + 1 ) x 4 x 3
2 x 1 x 4 x 3
2 / 1 x 4 x 3
( 3 + 1 + 4 ) x 3
( 3 - 1 ) x 4 x 3
( 4 x 1 + 4 ) x 3
( 4 / 1 + 4 ) x 3
( 5 - 1 + 4 ) x 3
1 x 2 x 4 x 3
( 2 + 2 + 4 ) x 3
( 2 x 2 + 4 ) x 3
( 4 - 2 ) x 4 x 3
4 / 2 x 4 x 3
( 6 - 2 + 4 ) x 3
( 6 x 2 - 4 ) x 3
( 8 / 2 + 4 ) x 3
9 x 2 x 4 / 3
( 1 + 3 + 4 ) x 3
( 4 x 3 - 4 ) x 3
( 5 - 3 ) x 4 x 3
6 x 3 x 4 / 3
6 / 3 x 4 x 3
( 7 - 3 + 4 ) x 3
( 9 + 3 - 4 ) x 3
( 1 x 4 + 4 ) x 3
( 3 x 4 - 4 ) x 3
( 6 - 4 ) x 4 x 3
( 8 + 4 - 4 ) x 3
( 8 - 4 + 4 ) x 3
8 x 4 / 4 x 3
8 / 4 x 4 x 3
5 x 5 - 4 + 3
( 7 + 5 - 4 ) x 3
( 7 - 5 ) x 4 x 3
( 9 - 5 + 4 ) x 3
( 2 x 6 - 4 ) x 3
3 x 6 x 4 / 3
( 6 + 6 - 4 ) x 3
( 8 - 6 ) x 4 x 3
( 5 + 7 - 4 ) x 3
( 9 - 7 ) x 4 x 3
( 4 + 8 - 4 ) x 3
4 x 8 / 4 x 3
9 + 8 + 4 + 3
2 x 9 x 4 / 3
( 3 + 9 - 4 ) x 3
8 + 9 + 4 + 3
( 9 + 9 ) x 4 / 3
( 2 + 1 + 5 ) x 3
( 3 x 1 + 5 ) x 3
( 3 / 1 + 5 ) x 3
( 4 - 1 + 5 ) x 3
( 1 + 2 + 5 ) x 3
( 5 - 2 + 5 ) x 3
( 6 / 2 + 5 ) x 3
8 x 2 + 5 + 3
( 1 x 3 + 5 ) x 3
( 6 - 3 + 5 ) x 3
( 9 / 3 + 5 ) x 3
4 x 4 + 5 + 3
( 7 - 4 + 5 ) x 3
8 x 4 - 5 - 3
( 9 + 4 - 5 ) x 3
( 8 + 5 - 5 ) x 3
( 8 - 5 + 5 ) x 3
8 x 5 / 5 x 3
8 / 5 x 5 x 3
( 7 + 6 - 5 ) x 3
( 9 - 6 + 5 ) x 3
( 6 + 7 - 5 ) x 3
9 + 7 + 5 + 3
2 x 8 + 5 + 3
4 x 8 - 5 - 3
( 5 + 8 - 5 ) x 3
5 x 8 / 5 x 3
8 + 8 + 5 + 3
( 4 + 9 - 5 ) x 3
7 + 9 + 5 + 3
( 1 + 1 + 6 ) x 3
( 2 x 1 + 6 ) x 3
( 2 / 1 + 6 ) x 3
( 3 - 1 + 6 ) x 3
( 1 x 2 + 6 ) x 3
( 4 - 2 + 6 ) x 3
( 4 / 2 + 6 ) x 3
6 x 2 x 6 / 3
( 7 x 2 - 6 ) x 3
7 / 2 x 6 + 3
9 / 2 x 6 - 3
4 x 3 x 6 / 3
4 / 3 x 6 x 3
( 5 - 3 + 6 ) x 3
5 x 3 + 6 + 3
( 6 / 3 + 6 ) x 3
7 x 3 + 6 - 3
( 9 + 3 ) x 6 / 3
9 x 3 - 6 + 3
3 x 4 x 6 / 3
( 6 - 4 + 6 ) x 3
( 8 + 4 ) x 6 / 3
( 8 / 4 + 6 ) x 3
3 x 5 + 6 + 3
( 7 + 5 ) x 6 / 3
( 7 - 5 + 6 ) x 3
( 9 + 5 - 6 ) x 3
2 x 6 x 6 / 3
( 6 + 6 ) x 6 / 3
( 8 + 6 - 6 ) x 3
( 8 - 6 + 6 ) x 3
8 x 6 / 6 x 3
8 / 6 x 6 x 3
9 + 6 + 6 + 3
( 2 x 7 - 6 ) x 3
3 x 7 + 6 - 3
( 5 + 7 ) x 6 / 3
( 7 + 7 - 6 ) x 3
8 + 7 + 6 + 3
( 9 - 7 + 6 ) x 3
( 4 + 8 ) x 6 / 3
( 6 + 8 - 6 ) x 3
6 x 8 / 6 x 3
7 + 8 + 6 + 3
( 3 + 9 ) x 6 / 3
3 x 9 - 6 + 3
( 5 + 9 - 6 ) x 3
6 + 9 + 6 + 3
( 1 x 1 + 7 ) x 3
( 1 / 1 + 7 ) x 3
( 2 + 1 ) x 7 + 3
( 2 - 1 + 7 ) x 3
3 x 1 x 7 + 3
3 / 1 x 7 + 3
( 4 - 1 ) x 7 + 3
( 1 + 2 ) x 7 + 3
( 2 / 2 + 7 ) x 3
( 3 - 2 + 7 ) x 3
( 5 - 2 ) x 7 + 3
6 / 2 x 7 + 3
7 x 2 + 7 + 3
1 x 3 x 7 + 3
( 3 / 3 + 7 ) x 3
( 4 - 3 + 7 ) x 3
( 5 x 3 - 7 ) x 3
( 6 - 3 ) x 7 + 3
9 / 3 x 7 + 3
( 4 / 4 + 7 ) x 3
( 5 - 4 + 7 ) x 3
5 x 4 + 7 - 3
( 7 - 4 ) x 7 + 3
7 x 4 - 7 + 3
( 3 x 5 - 7 ) x 3
4 x 5 + 7 - 3
( 5 / 5 + 7 ) x 3
( 6 - 5 + 7 ) x 3
( 8 - 5 ) x 7 + 3
9 + 5 + 7 + 3
( 6 / 6 + 7 ) x 3
( 7 - 6 + 7 ) x 3
8 + 6 + 7 + 3
( 9 + 6 - 7 ) x 3
( 9 - 6 ) x 7 + 3
2 x 7 + 7 + 3
4 x 7 - 7 + 3
7 + 7 + 7 + 3
( 7 / 7 + 7 ) x 3
( 8 + 7 - 7 ) x 3
( 8 - 7 + 7 ) x 3
8 x 7 / 7 x 3
8 / 7 x 7 x 3
6 + 8 + 7 + 3
( 7 + 8 - 7 ) x 3
7 x 8 / 7 x 3
( 8 / 8 + 7 ) x 3
( 9 - 8 + 7 ) x 3
5 + 9 + 7 + 3
( 6 + 9 - 7 ) x 3
( 9 / 9 + 7 ) x 3
( 1 - 1 + 8 ) x 3
1 x 1 x 8 x 3
1 / 1 x 8 x 3
( 2 - 1 ) x 8 x 3
( 8 + 1 ) x 8 / 3
9 x 1 x 8 / 3
9 / 1 x 8 / 3
( 2 - 2 + 8 ) x 3
2 / 2 x 8 x 3
( 3 - 2 ) x 8 x 3
( 7 + 2 ) x 8 / 3
( 8 x 2 - 8 ) x 3
( 3 - 3 + 8 ) x 3
3 x 3 x 8 / 3
3 / 3 x 8 x 3
( 4 - 3 ) x 8 x 3
( 6 + 3 ) x 8 / 3
( 4 - 4 + 8 ) x 3
( 4 x 4 - 8 ) x 3
4 / 4 x 8 x 3
( 5 + 4 ) x 8 / 3
( 5 - 4 ) x 8 x 3
9 + 4 + 8 + 3
( 4 + 5 ) x 8 / 3
( 5 - 5 + 8 ) x 3
5 / 5 x 8 x 3
( 6 - 5 ) x 8 x 3
7 x 5 - 8 - 3
8 + 5 + 8 + 3
( 3 + 6 ) x 8 / 3
( 6 - 6 + 8 ) x 3
6 / 6 x 8 x 3
7 + 6 + 8 + 3
( 7 - 6 ) x 8 x 3
( 2 + 7 ) x 8 / 3
5 x 7 - 8 - 3
6 + 7 + 8 + 3
( 7 - 7 + 8 ) x 3
7 / 7 x 8 x 3
( 8 - 7 ) x 8 x 3
( 9 + 7 - 8 ) x 3
( 1 + 8 ) x 8 / 3
( 2 x 8 - 8 ) x 3
5 + 8 + 8 + 3
( 8 + 8 - 8 ) x 3
( 8 - 8 + 8 ) x 3
( 8 x 8 + 8 ) / 3
8 x 8 / 8 x 3
8 / 8 x 8 x 3
( 9 - 8 ) x 8 x 3
1 x 9 x 8 / 3
4 + 9 + 8 + 3
( 7 + 9 - 8 ) x 3
( 9 - 9 + 8 ) x 3
9 / 9 x 8 x 3
( 2 + 1 ) x 9 - 3
3 x 1 x 9 - 3
3 / 1 x 9 - 3
( 4 - 1 ) x 9 - 3
( 7 + 1 ) x 9 / 3
8 x 1 x 9 / 3
8 / 1 x 9 / 3
( 9 - 1 ) x 9 / 3
( 1 + 2 ) x 9 - 3
( 1 - 2 + 9 ) x 3
4 x 2 x 9 / 3
( 5 - 2 ) x 9 - 3
( 6 + 2 ) x 9 / 3
6 x 2 + 9 + 3
6 / 2 x 9 - 3
9 x 2 + 9 - 3
1 x 3 x 9 - 3
( 2 - 3 + 9 ) x 3
4 x 3 + 9 + 3
( 5 + 3 ) x 9 / 3
( 6 - 3 ) x 9 - 3
6 x 3 + 9 - 3
7 / 3 x 9 + 3
9 + 3 + 9 + 3
9 / 3 x 9 - 3
2 x 4 x 9 / 3
( 3 - 4 + 9 ) x 3
3 x 4 + 9 + 3
( 4 + 4 ) x 9 / 3
( 7 - 4 ) x 9 - 3
8 + 4 + 9 + 3
9 x 4 - 9 - 3
( 3 + 5 ) x 9 / 3
( 4 - 5 + 9 ) x 3
6 x 5 - 9 + 3
7 + 5 + 9 + 3
( 8 - 5 ) x 9 - 3
( 2 + 6 ) x 9 / 3
2 x 6 + 9 + 3
3 x 6 + 9 - 3
( 5 - 6 + 9 ) x 3
5 x 6 - 9 + 3
6 + 6 + 9 + 3
6 x 6 - 9 - 3
( 9 - 6 ) x 9 - 3
( 1 + 7 ) x 9 / 3
5 + 7 + 9 + 3
( 6 - 7 + 9 ) x 3
( 9 x 7 + 9 ) / 3
1 x 8 x 9 / 3
4 + 8 + 9 + 3
( 7 - 8 + 9 ) x 3
( 9 + 8 - 9 ) x 3
9 x 8 / 9 x 3
2 x 9 + 9 - 3
3 + 9 + 9 + 3
4 x 9 - 9 - 3
( 7 x 9 + 9 ) / 3
( 8 + 9 - 9 ) x 3
( 8 - 9 + 9 ) x 3
8 x 9 / 9 x 3
8 / 9 x 9 x 3
9 + 9 + 9 - 3
( 9 x 9 - 9 ) / 3
( 4 + 1 + 1 ) x 4
( 5 + 1 ) x 1 x 4
( 5 + 1 ) / 1 x 4
( 5 x 1 + 1 ) x 4
( 5 / 1 + 1 ) x 4
( 6 + 1 - 1 ) x 4
( 6 - 1 + 1 ) x 4
6 x 1 x 1 x 4
6 x 1 / 1 x 4
6 / 1 x 1 x 4
6 / 1 / 1 x 4
( 7 - 1 ) x 1 x 4
( 7 - 1 ) / 1 x 4
( 7 x 1 - 1 ) x 4
( 7 / 1 - 1 ) x 4
( 8 - 1 - 1 ) x 4
( 3 + 2 + 1 ) x 4
3 x 2 x 1 x 4
3 x 2 / 1 x 4
( 4 + 2 ) x 1 x 4
( 4 + 2 ) / 1 x 4
( 5 + 2 - 1 ) x 4
( 7 - 2 + 1 ) x 4
( 8 - 2 ) x 1 x 4
( 8 - 2 ) / 1 x 4
( 9 - 2 - 1 ) x 4
( 2 + 3 + 1 ) x 4
2 x 3 x 1 x 4
2 x 3 / 1 x 4
( 3 + 3 ) x 1 x 4
( 3 + 3 ) / 1 x 4
( 4 + 3 - 1 ) x 4
7 x 3 - 1 + 4
( 8 - 3 + 1 ) x 4
( 9 - 3 ) x 1 x 4
( 9 - 3 ) / 1 x 4
9 x 3 + 1 - 4
( 1 + 4 + 1 ) x 4
( 2 + 4 ) x 1 x 4
( 2 + 4 ) / 1 x 4
( 3 + 4 - 1 ) x 4
5 x 4 x 1 + 4
5 x 4 / 1 + 4
7 x 4 x 1 - 4
7 x 4 / 1 - 4
( 9 - 4 + 1 ) x 4
( 1 + 5 ) x 1 x 4
( 1 + 5 ) / 1 x 4
( 1 x 5 + 1 ) x 4
( 2 + 5 - 1 ) x 4
4 x 5 x 1 + 4
4 x 5 / 1 + 4
( 1 + 6 - 1 ) x 4
1 x 6 x 1 x 4
1 x 6 / 1 x 4
( 1 x 7 - 1 ) x 4
3 x 7 - 1 + 4
4 x 7 x 1 - 4
4 x 7 / 1 - 4
3 x 9 + 1 - 4
( 2 + 1 ) x 2 x 4
( 3 + 1 + 2 ) x 4
3 x 1 x 2 x 4
3 / 1 x 2 x 4
( 4 - 1 ) x 2 x 4
( 4 x 1 + 2 ) x 4
( 4 / 1 + 2 ) x 4
( 5 - 1 + 2 ) x 4
( 7 + 1 - 2 ) x 4
( 8 x 1 - 2 ) x 4
( 8 / 1 - 2 ) x 4
( 9 + 1 ) x 2 + 4
( 9 - 1 - 2 ) x 4
( 1 + 2 ) x 2 x 4
( 2 + 2 + 2 ) x 4
( 2 x 2 + 2 ) x 4
( 4 x 2 - 2 ) x 4
( 5 - 2 ) x 2 x 4
5 x 2 x 2 + 4
( 6 + 2 - 2 ) x 4
( 6 - 2 + 2 ) x 4
6 x 2 / 2 x 4
6 / 2 x 2 x 4
7 x 2 x 2 - 4
( 8 + 2 ) x 2 + 4
( 8 / 2 + 2 ) x 4
9 x 2 + 2 + 4
( 1 + 3 + 2 ) x 4
1 x 3 x 2 x 4
4 x 3 / 2 x 4
( 5 + 3 - 2 ) x 4
( 6 - 3 ) x 2 x 4
6 x 3 + 2 + 4
( 7 + 3 ) x 2 + 4
( 7 - 3 + 2 ) x 4
( 9 + 3 ) / 2 x 4
9 / 3 x 2 x 4
( 1 x 4 + 2 ) x 4
( 2 x 4 - 2 ) x 4
3 x 4 / 2 x 4
( 4 + 4 - 2 ) x 4
( 6 + 4 ) x 2 + 4
( 7 - 4 ) x 2 x 4
( 8 + 4 ) / 2 x 4
( 8 - 4 + 2 ) x 4
2 x 5 x 2 + 4
( 3 + 5 - 2 ) x 4
( 5 + 5 ) x 2 + 4
6 x 5 - 2 - 4
( 7 + 5 ) / 2 x 4
( 8 - 5 ) x 2 x 4
8 x 5 / 2 + 4
( 9 + 5 ) x 2 - 4
( 9 - 5 + 2 ) x 4
( 2 + 6 - 2 ) x 4
2 x 6 / 2 x 4
3 x 6 + 2 + 4
( 4 + 6 ) x 2 + 4
5 x 6 - 2 - 4
( 6 + 6 ) / 2 x 4
( 8 + 6 ) x 2 - 4
8 x 6 x 2 / 4
( 9 - 6 ) x 2 x 4
( 1 + 7 - 2 ) x 4
2 x 7 x 2 - 4
( 3 + 7 ) x 2 + 4
( 5 + 7 ) / 2 x 4
( 7 + 7 ) x 2 - 4
8 x 7 / 2 - 4
( 1 x 8 - 2 ) x 4
( 2 + 8 ) x 2 + 4
( 4 + 8 ) / 2 x 4
5 x 8 / 2 + 4
( 6 + 8 ) x 2 - 4
6 x 8 x 2 / 4
7 x 8 / 2 - 4
( 1 + 9 ) x 2 + 4
2 x 9 + 2 + 4
( 3 + 9 ) / 2 x 4
( 5 + 9 ) x 2 - 4
9 + 9 + 2 + 4
( 1 + 1 ) x 3 x 4
( 2 + 1 + 3 ) x 4
2 x 1 x 3 x 4
2 / 1 x 3 x 4
( 3 - 1 ) x 3 x 4
( 3 x 1 + 3 ) x 4
( 3 / 1 + 3 ) x 4
( 4 - 1 + 3 ) x 4
( 8 + 1 - 3 ) x 4
( 9 x 1 - 3 ) x 4
( 9 / 1 - 3 ) x 4
( 1 + 2 + 3 ) x 4
1 x 2 x 3 x 4
( 4 - 2 ) x 3 x 4
4 / 2 x 3 x 4
( 5 - 2 + 3 ) x 4
( 6 / 2 + 3 ) x 4
( 7 + 2 - 3 ) x 4
9 x 2 / 3 x 4
( 1 x 3 + 3 ) x 4
( 3 x 3 - 3 ) x 4
( 5 - 3 ) x 3 x 4
( 6 + 3 - 3 ) x 4
( 6 - 3 + 3 ) x 4
6 x 3 / 3 x 4
6 / 3 x 3 x 4
( 9 / 3 + 3 ) x 4
( 5 + 4 - 3 ) x 4
( 6 - 4 ) x 3 x 4
( 7 - 4 + 3 ) x 4
8 x 4 x 3 / 4
8 / 4 x 3 x 4
( 4 + 5 - 3 ) x 4
5 x 5 + 3 - 4
( 7 - 5 ) x 3 x 4
( 8 - 5 + 3 ) x 4
( 3 + 6 - 3 ) x 4
3 x 6 / 3 x 4
( 8 - 6 ) x 3 x 4
( 9 - 6 + 3 ) x 4
( 2 + 7 - 3 ) x 4
( 9 - 7 ) x 3 x 4
( 1 + 8 - 3 ) x 4
4 x 8 x 3 / 4
9 + 8 + 3 + 4
( 1 x 9 - 3 ) x 4
2 x 9 / 3 x 4
8 + 9 + 3 + 4
( 9 + 9 ) / 3 x 4
( 1 + 1 + 4 ) x 4
( 2 x 1 + 4 ) x 4
( 2 / 1 + 4 ) x 4
( 3 - 1 + 4 ) x 4
( 4 + 1 ) x 4 + 4
5 x 1 x 4 + 4
5 / 1 x 4 + 4
( 6 + 1 ) x 4 - 4
( 6 - 1 ) x 4 + 4
7 x 1 x 4 - 4
7 / 1 x 4 - 4
( 8 - 1 ) x 4 - 4
( 9 + 1 - 4 ) x 4
( 1 x 2 + 4 ) x 4
( 3 + 2 ) x 4 + 4
3 / 2 x 4 x 4
( 4 - 2 + 4 ) x 4
( 4 / 2 + 4 ) x 4
( 5 + 2 ) x 4 - 4
( 5 x 2 - 4 ) x 4
( 7 - 2 ) x 4 + 4
( 8 + 2 - 4 ) x 4
8 x 2 + 4 + 4
( 9 - 2 ) x 4 - 4
( 2 + 3 ) x 4 + 4
( 4 + 3 ) x 4 - 4
( 5 - 3 + 4 ) x 4
( 6 / 3 + 4 ) x 4
( 7 + 3 - 4 ) x 4
( 8 - 3 ) x 4 + 4
8 x 3 + 4 - 4
8 x 3 - 4 + 4
8 x 3 x 4 / 4
8 x 3 / 4 x 4
( 1 + 4 ) x 4 + 4
( 3 + 4 ) x 4 - 4
4 x 4 + 4 + 4
( 6 + 4 - 4 ) x 4
( 6 - 4 + 4 ) x 4
6 x 4 + 4 - 4
6 x 4 - 4 + 4
6 x 4 x 4 / 4
6 x 4 / 4 x 4
6 / 4 x 4 x 4
8 x 4 - 4 - 4
( 8 / 4 + 4 ) x 4
( 9 - 4 ) x 4 + 4
1 x 5 x 4 + 4
( 2 + 5 ) x 4 - 4
( 2 x 5 - 4 ) x 4
( 5 + 5 - 4 ) x 4
( 7 - 5 + 4 ) x 4
( 1 + 6 ) x 4 - 4
( 4 + 6 - 4 ) x 4
4 x 6 + 4 - 4
4 x 6 - 4 + 4
4 x 6 x 4 / 4
4 x 6 / 4 x 4
( 8 - 6 + 4 ) x 4
9 / 6 x 4 x 4
1 x 7 x 4 - 4
( 3 + 7 - 4 ) x 4
9 + 7 + 4 + 4
( 9 - 7 + 4 ) x 4
( 2 + 8 - 4 ) x 4
2 x 8 + 4 + 4
3 x 8 + 4 - 4
3 x 8 - 4 + 4
3 x 8 x 4 / 4
3 x 8 / 4 x 4
4 x 8 - 4 - 4
8 + 8 + 4 + 4
( 1 + 9 - 4 ) x 4
7 + 9 + 4 + 4
( 1 x 1 + 5 ) x 4
( 1 / 1 + 5 ) x 4
( 2 - 1 + 5 ) x 4
( 3 + 1 ) x 5 + 4
4 x 1 x 5 + 4
4 / 1 x 5 + 4
( 5 - 1 ) x 5 + 4
( 2 + 2 ) x 5 + 4
2 x 2 x 5 + 4
( 2 / 2 + 5 ) x 4
( 3 - 2 + 5 ) x 4
( 6 - 2 ) x 5 + 4
8 / 2 x 5 + 4
( 9 + 2 - 5 ) x 4
( 1 + 3 ) x 5 + 4
( 3 / 3 + 5 ) x 4
( 4 - 3 + 5 ) x 4
5 x 3 + 5 + 4
( 7 - 3 ) x 5 + 4
( 8 + 3 - 5 ) x 4
1 x 4 x 5 + 4
( 4 / 4 + 5 ) x 4
( 5 - 4 + 5 ) x 4
( 7 + 4 - 5 ) x 4
( 8 - 4 ) x 5 + 4
3 x 5 + 5 + 4
5 x 5 - 5 + 4
( 5 / 5 + 5 ) x 4
( 6 + 5 - 5 ) x 4
( 6 - 5 + 5 ) x 4
6 x 5 / 5 x 4
6 / 5 x 5 x 4
( 9 - 5 ) x 5 + 4
( 5 + 6 - 5 ) x 4
5 x 6 / 5 x 4
( 6 / 6 + 5 ) x 4
( 7 - 6 + 5 ) x 4
9 + 6 + 5 + 4
( 4 + 7 - 5 ) x 4
( 7 / 7 + 5 ) x 4
8 + 7 + 5 + 4
( 8 - 7 + 5 ) x 4
( 3 + 8 - 5 ) x 4
7 + 8 + 5 + 4
( 8 / 8 + 5 ) x 4
( 9 - 8 + 5 ) x 4
( 2 + 9 - 5 ) x 4
6 + 9 + 5 + 4
( 9 / 9 + 5 ) x 4
( 1 - 1 + 6 ) x 4
1 x 1 x 6 x 4
1 / 1 x 6 x 4
( 2 - 1 ) x 6 x 4
( 2 - 2 + 6 ) x 4
2 / 2 x 6 x 4
( 3 - 2 ) x 6 x 4
( 6 x 2 - 6 ) x 4
7 x 2 + 6 + 4
8 x 2 x 6 / 4
( 3 - 3 + 6 ) x 4
3 / 3 x 6 x 4
( 4 - 3 ) x 6 x 4
( 4 x 3 - 6 ) x 4
( 9 + 3 - 6 ) x 4
( 3 x 4 - 6 ) x 4
( 4 - 4 + 6 ) x 4
4 x 4 x 6 / 4
4 / 4 x 6 x 4
( 5 - 4 ) x 6 x 4
( 8 + 4 - 6 ) x 4
9 x 4 / 6 x 4
( 5 - 5 + 6 ) x 4
5 / 5 x 6 x 4
( 6 - 5 ) x 6 x 4
( 7 + 5 - 6 ) x 4
9 + 5 + 6 + 4
( 2 x 6 - 6 ) x 4
( 6 + 6 - 6 ) x 4
( 6 - 6 + 6 ) x 4
6 x 6 / 6 x 4
6 / 6 x 6 x 4
( 7 - 6 ) x 6 x 4
8 + 6 + 6 + 4
2 x 7 + 6 + 4
( 5 + 7 - 6 ) x 4
7 + 7 + 6 + 4
( 7 - 7 + 6 ) x 4
7 / 7 x 6 x 4
( 8 - 7 ) x 6 x 4
( 9 + 7 ) x 6 / 4
2 x 8 x 6 / 4
( 4 + 8 - 6 ) x 4
6 + 8 + 6 + 4
( 8 + 8 ) x 6 / 4
( 8 - 8 + 6 ) x 4
8 / 8 x 6 x 4
( 9 - 8 ) x 6 x 4
( 3 + 9 - 6 ) x 4
4 x 9 / 6 x 4
5 + 9 + 6 + 4
( 7 + 9 ) x 6 / 4
( 9 - 9 + 6 ) x 4
9 / 9 x 6 x 4
( 3 + 1 ) x 7 - 4
4 x 1 x 7 - 4
4 / 1 x 7 - 4
( 5 - 1 ) x 7 - 4
( 1 - 2 + 7 ) x 4
( 2 + 2 ) x 7 - 4
2 x 2 x 7 - 4
( 6 - 2 ) x 7 - 4
8 / 2 x 7 - 4
( 1 + 3 ) x 7 - 4
( 2 - 3 + 7 ) x 4
( 7 - 3 ) x 7 - 4
7 x 3 + 7 - 4
9 x 3 - 7 + 4
1 x 4 x 7 - 4
( 3 - 4 + 7 ) x 4
( 8 - 4 ) x 7 - 4
9 + 4 + 7 + 4
( 9 + 4 - 7 ) x 4
( 4 - 5 + 7 ) x 4
7 x 5 - 7 - 4
8 + 5 + 7 + 4
( 8 + 5 - 7 ) x 4
( 9 - 5 ) x 7 - 4
( 5 - 6 + 7 ) x 4
7 + 6 + 7 + 4
( 7 + 6 - 7 ) x 4
7 x 6 / 7 x 4
3 x 7 + 7 - 4
5 x 7 - 7 - 4
6 + 7 + 7 + 4
( 6 + 7 - 7 ) x 4
( 6 - 7 + 7 ) x 4
6 x 7 / 7 x 4
6 / 7 x 7 x 4
5 + 8 + 7 + 4
( 5 + 8 - 7 ) x 4
( 7 - 8 + 7 ) x 4
3 x 9 - 7 + 4
4 + 9 + 7 + 4
( 4 + 9 - 7 ) x 4
( 8 - 9 + 7 ) x 4
5 / 2 x 8 + 4
6 x 2 + 8 + 4
6 x 2 x 8 / 4
( 7 x 2 - 8 ) x 4
7 / 2 x 8 - 4
( 1 - 3 + 8 ) x 4
4 x 3 + 8 + 4
4 x 3 x 8 / 4
9 + 3 + 8 + 4
( 9 + 3 ) x 8 / 4
( 2 - 4 + 8 ) x 4
3 x 4 + 8 + 4
3 x 4 x 8 / 4
3 / 4 x 8 x 4
5 x 4 + 8 - 4
7 x 4 - 8 + 4
8 + 4 + 8 + 4
( 8 + 4 ) x 8 / 4
9 x 4 - 8 - 4
( 3 - 5 + 8 ) x 4
4 x 5 + 8 - 4
7 + 5 + 8 + 4
( 7 + 5 ) x 8 / 4
( 9 + 5 - 8 ) x 4
2 x 6 + 8 + 4
2 x 6 x 8 / 4
( 4 - 6 + 8 ) x 4
6 + 6 + 8 + 4
( 6 + 6 ) x 8 / 4
6 x 6 - 8 - 4
( 8 + 6 - 8 ) x 4
8 x 6 / 8 x 4
( 2 x 7 - 8 ) x 4
4 x 7 - 8 + 4
5 + 7 + 8 + 4
( 5 + 7 ) x 8 / 4
( 5 - 7 + 8 ) x 4
( 7 + 7 - 8 ) x 4
4 + 8 + 8 + 4
( 4 + 8 ) x 8 / 4
( 6 + 8 - 8 ) x 4
( 6 - 8 + 8 ) x 4
6 x 8 / 8 x 4
6 / 8 x 8 x 4
3 + 9 + 8 + 4
( 3 + 9 ) x 8 / 4
4 x 9 - 8 - 4
( 5 + 9 - 8 ) x 4
( 7 - 9 + 8 ) x 4
9 + 2 + 9 + 4
2 / 3 x 9 x 4
( 5 x 3 - 9 ) x 4
8 + 3 + 9 + 4
( 1 - 4 + 9 ) x 4
7 + 4 + 9 + 4
( 2 - 5 + 9 ) x 4
( 3 x 5 - 9 ) x 4
6 + 5 + 9 + 4
( 3 - 6 + 9 ) x 4
4 / 6 x 9 x 4
5 + 6 + 9 + 4
( 9 + 6 - 9 ) x 4
9 x 6 / 9 x 4
4 + 7 + 9 + 4
( 4 - 7 + 9 ) x 4
( 8 + 7 - 9 ) x 4
3 + 8 + 9 + 4
( 5 - 8 + 9 ) x 4
( 7 + 8 - 9 ) x 4
2 + 9 + 9 + 4
( 6 + 9 - 9 ) x 4
( 6 - 9 + 9 ) x 4
6 x 9 / 9 x 4
6 / 9 x 9 x 4
9 x 2 + 1 + 5
6 x 3 + 1 + 5
5 x 4 - 1 + 5
7 x 4 + 1 - 5
4 x 5 - 1 + 5
6 x 5 - 1 - 5
3 x 6 + 1 + 5
5 x 6 - 1 - 5
4 x 7 + 1 - 5
2 x 9 + 1 + 5
9 + 9 + 1 + 5
7 x 3 - 2 + 5
9 x 3 + 2 - 5
3 x 7 - 2 + 5
9 + 8 + 2 + 5
3 x 9 + 2 - 5
8 + 9 + 2 + 5
8 x 2 + 3 + 5
4 x 4 + 3 + 5
8 x 4 - 3 - 5
8 x 5 x 3 / 5
8 / 5 x 3 x 5
( 9 / 5 + 3 ) x 5
9 + 7 + 3 + 5
2 x 8 + 3 + 5
4 x 8 - 3 - 5
5 x 8 x 3 / 5
8 + 8 + 3 + 5
7 + 9 + 3 + 5
5 x 3 + 4 + 5
3 x 5 + 4 + 5
( 4 / 5 + 4 ) x 5
5 x 5 + 4 - 5
6 x 5 x 4 / 5
6 / 5 x 4 x 5
5 x 6 x 4 / 5
9 + 6 + 4 + 5
8 + 7 + 4 + 5
7 + 8 + 4 + 5
6 + 9 + 4 + 5
7 x 2 + 5 + 5
8 x 3 + 5 - 5
8 x 3 - 5 + 5
8 x 3 x 5 / 5
8 x 3 / 5 x 5
6 x 4 + 5 - 5
6 x 4 - 5 + 5
6 x 4 x 5 / 5
6 x 4 / 5 x 5
9 + 5 + 5 + 5
4 x 6 + 5 - 5
4 x 6 - 5 + 5
4 x 6 x 5 / 5
4 x 6 / 5 x 5
8 + 6 + 5 + 5
2 x 7 + 5 + 5
7 + 7 + 5 + 5
3 x 8 + 5 - 5
3 x 8 - 5 + 5
3 x 8 x 5 / 5
3 x 8 / 5 x 5
6 + 8 + 5 + 5
5 + 9 + 5 + 5
5 x 4 x 6 / 5
9 + 4 + 6 + 5
4 x 5 x 6 / 5
4 / 5 x 6 x 5
5 x 5 - 6 + 5
7 x 5 - 6 - 5
8 + 5 + 6 + 5
7 + 6 + 6 + 5
5 x 7 - 6 - 5
6 + 7 + 6 + 5
5 + 8 + 6 + 5
4 + 9 + 6 + 5
6 x 2 + 7 + 5
4 x 3 + 7 + 5
9 + 3 + 7 + 5
3 x 4 + 7 + 5
8 + 4 + 7 + 5
9 x 4 - 7 - 5
7 + 5 + 7 + 5
2 x 6 + 7 + 5
6 + 6 + 7 + 5
6 x 6 - 7 - 5
5 + 7 + 7 + 5
4 + 8 + 7 + 5
3 + 9 + 7 + 5
4 x 9 - 7 - 5
9 + 2 + 8 + 5
5 x 3 x 8 / 5
7 x 3 + 8 - 5
8 + 3 + 8 + 5
9 x 3 - 8 + 5
7 + 4 + 8 + 5
3 x 5 x 8 / 5
3 / 5 x 8 x 5
6 + 5 + 8 + 5
5 + 6 + 8 + 5
( 9 + 6 ) x 8 / 5
3 x 7 + 8 - 5
4 + 7 + 8 + 5
( 8 + 7 ) x 8 / 5
3 + 8 + 8 + 5
( 7 + 8 ) x 8 / 5
2 + 9 + 8 + 5
3 x 9 - 8 + 5
( 6 + 9 ) x 8 / 5
9 + 1 + 9 + 5
5 x 2 + 9 + 5
8 + 2 + 9 + 5
7 + 3 + 9 + 5
5 x 4 + 9 - 5
6 + 4 + 9 + 5
7 x 4 - 9 + 5
2 x 5 + 9 + 5
4 x 5 + 9 - 5
5 + 5 + 9 + 5
4 + 6 + 9 + 5
3 + 7 + 9 + 5
4 x 7 - 9 + 5
2 + 8 + 9 + 5
1 + 9 + 9 + 5
( 2 + 1 + 1 ) x 6
( 3 + 1 ) x 1 x 6
( 3 + 1 ) / 1 x 6
( 3 x 1 + 1 ) x 6
( 3 / 1 + 1 ) x 6
( 4 + 1 - 1 ) x 6
( 4 - 1 + 1 ) x 6
4 x 1 x 1 x 6
4 x 1 / 1 x 6
4 / 1 x 1 x 6
4 / 1 / 1 x 6
( 5 - 1 ) x 1 x 6
( 5 - 1 ) / 1 x 6
( 5 x 1 - 1 ) x 6
( 5 / 1 - 1 ) x 6
( 6 - 1 - 1 ) x 6
( 1 + 2 + 1 ) x 6
( 2 + 2 ) x 1 x 6
( 2 + 2 ) / 1 x 6
2 x 2 x 1 x 6
2 x 2 / 1 x 6
( 3 + 2 - 1 ) x 6
( 5 - 2 + 1 ) x 6
( 6 - 2 ) x 1 x 6
( 6 - 2 ) / 1 x 6
( 6 / 2 + 1 ) x 6
( 7 - 2 - 1 ) x 6
8 / 2 x 1 x 6
8 / 2 / 1 x 6
9 x 2 x 1 + 6
9 x 2 / 1 + 6
( 1 + 3 ) x 1 x 6
( 1 + 3 ) / 1 x 6
( 1 x 3 + 1 ) x 6
( 2 + 3 - 1 ) x 6
( 6 - 3 + 1 ) x 6
6 x 3 x 1 + 6
6 x 3 / 1 + 6
( 7 - 3 ) x 1 x 6
( 7 - 3 ) / 1 x 6
( 8 - 3 - 1 ) x 6
( 9 / 3 + 1 ) x 6
( 1 + 4 - 1 ) x 6
1 x 4 x 1 x 6
1 x 4 / 1 x 6
( 7 - 4 + 1 ) x 6
( 8 - 4 ) x 1 x 6
( 8 - 4 ) / 1 x 6
( 9 - 4 - 1 ) x 6
( 1 x 5 - 1 ) x 6
6 x 5 x 1 - 6
6 x 5 / 1 - 6
( 8 - 5 + 1 ) x 6
( 9 - 5 ) x 1 x 6
( 9 - 5 ) / 1 x 6
3 x 6 x 1 + 6
3 x 6 / 1 + 6
5 x 6 x 1 - 6
5 x 6 / 1 - 6
( 9 - 6 + 1 ) x 6
9 + 8 + 1 + 6
2 x 9 x 1 + 6
2 x 9 / 1 + 6
8 + 9 + 1 + 6
( 9 + 9 ) x 1 + 6
( 9 + 9 ) / 1 + 6
( 1 + 1 + 2 ) x 6
( 1 + 1 ) x 2 x 6
( 2 x 1 + 2 ) x 6
2 x 1 x 2 x 6
( 2 / 1 + 2 ) x 6
2 / 1 x 2 x 6
( 3 - 1 + 2 ) x 6
( 3 - 1 ) x 2 x 6
( 5 + 1 - 2 ) x 6
( 6 x 1 - 2 ) x 6
( 6 / 1 - 2 ) x 6
( 7 + 1 ) / 2 x 6
( 7 - 1 - 2 ) x 6
( 8 + 1 ) x 2 + 6
8 x 1 / 2 x 6
8 / 1 / 2 x 6
( 9 - 1 ) / 2 x 6
9 x 1 x 2 + 6
9 / 1 x 2 + 6
( 1 x 2 + 2 ) x 6
1 x 2 x 2 x 6
( 3 x 2 - 2 ) x 6
( 4 + 2 - 2 ) x 6
( 4 - 2 + 2 ) x 6
( 4 - 2 ) x 2 x 6
4 x 2 / 2 x 6
( 4 / 2 + 2 ) x 6
4 / 2 x 2 x 6
( 6 + 2 ) / 2 x 6
( 7 + 2 ) x 2 + 6
( 8 - 2 - 2 ) x 6
8 x 2 + 2 + 6
( 2 x 3 - 2 ) x 6
( 3 + 3 - 2 ) x 6
3 x 3 x 2 + 6
( 5 + 3 ) / 2 x 6
( 5 - 3 + 2 ) x 6
( 5 - 3 ) x 2 x 6
5 x 3 x 2 - 6
( 6 + 3 ) x 2 + 6
( 6 / 3 + 2 ) x 6
6 / 3 x 2 x 6
( 9 - 3 - 2 ) x 6
( 2 + 4 - 2 ) x 6
2 x 4 / 2 x 6
( 4 + 4 ) / 2 x 6
4 x 4 + 2 + 6
( 5 + 4 ) x 2 + 6
5 x 4 - 2 + 6
( 6 - 4 + 2 ) x 6
( 6 - 4 ) x 2 x 6
7 x 4 + 2 - 6
8 x 4 - 2 - 6
( 8 / 4 + 2 ) x 6
8 / 4 x 2 x 6
9 x 4 / 2 + 6
( 1 + 5 - 2 ) x 6
( 3 + 5 ) / 2 x 6
3 x 5 x 2 - 6
( 4 + 5 ) x 2 + 6
4 x 5 - 2 + 6
( 7 - 5 + 2 ) x 6
( 7 - 5 ) x 2 x 6
( 1 x 6 - 2 ) x 6
( 2 + 6 ) / 2 x 6
( 3 + 6 ) x 2 + 6
6 x 6 / 2 + 6
( 8 - 6 + 2 ) x 6
( 8 - 6 ) x 2 x 6
( 9 + 6 ) x 2 - 6
( 1 + 7 ) / 2 x 6
( 2 + 7 ) x 2 + 6
4 x 7 + 2 - 6
( 8 + 7 ) x 2 - 6
9 + 7 + 2 + 6
( 9 - 7 + 2 ) x 6
( 9 - 7 ) x 2 x 6
( 1 + 8 ) x 2 + 6
1 x 8 / 2 x 6
2 x 8 + 2 + 6
4 x 8 - 2 - 6
( 7 + 8 ) x 2 - 6
8 + 8 + 2 + 6
9 x 8 x 2 / 6
1 x 9 x 2 + 6
4 x 9 / 2 + 6
( 6 + 9 ) x 2 - 6
7 + 9 + 2 + 6
8 x 9 x 2 / 6
( 1 x 1 + 3 ) x 6
( 1 / 1 + 3 ) x 6
( 2 - 1 + 3 ) x 6
( 5 + 1 ) x 3 + 6
( 6 + 1 - 3 ) x 6
6 x 1 x 3 + 6
6 / 1 x 3 + 6
( 7 - 1 ) x 3 + 6
( 7 x 1 - 3 ) x 6
( 7 / 1 - 3 ) x 6
( 8 - 1 - 3 ) x 6
( 9 + 1 ) x 3 - 6
( 2 / 2 + 3 ) x 6
( 3 - 2 + 3 ) x 6
3 x 2 x 3 + 6
( 4 + 2 ) x 3 + 6
( 5 + 2 - 3 ) x 6
5 x 2 x 3 - 6
6 x 2 / 3 x 6
( 8 + 2 ) x 3 - 6
( 8 - 2 ) x 3 + 6
( 9 - 2 - 3 ) x 6
2 x 3 x 3 + 6
( 3 + 3 ) x 3 + 6
( 3 / 3 + 3 ) x 6
( 4 + 3 - 3 ) x 6
( 4 - 3 + 3 ) x 6
4 x 3 / 3 x 6
4 / 3 x 3 x 6
5 x 3 + 3 + 6
( 7 + 3 ) x 3 - 6
7 x 3 - 3 + 6
( 9 + 3 ) / 3 x 6
( 9 - 3 ) x 3 + 6
9 x 3 + 3 - 6
( 2 + 4 ) x 3 + 6
( 3 + 4 - 3 ) x 6
3 x 4 / 3 x 6
( 4 / 4 + 3 ) x 6
( 5 - 4 + 3 ) x 6
( 6 + 4 ) x 3 - 6
( 8 + 4 ) / 3 x 6
( 1 + 5 ) x 3 + 6
( 2 + 5 - 3 ) x 6
2 x 5 x 3 - 6
3 x 5 + 3 + 6
( 5 + 5 ) x 3 - 6
( 5 / 5 + 3 ) x 6
( 6 - 5 + 3 ) x 6
( 7 + 5 ) / 3 x 6
( 1 + 6 - 3 ) x 6
1 x 6 x 3 + 6
2 x 6 / 3 x 6
( 4 + 6 ) x 3 - 6
( 6 + 6 ) / 3 x 6
( 6 / 6 + 3 ) x 6
( 7 - 6 + 3 ) x 6
8 x 6 x 3 / 6
8 / 6 x 3 x 6
9 + 6 + 3 + 6
9 x 6 / 3 + 6
( 1 x 7 - 3 ) x 6
( 3 + 7 ) x 3 - 6
3 x 7 - 3 + 6
( 5 + 7 ) / 3 x 6
( 7 / 7 + 3 ) x 6
8 + 7 + 3 + 6
( 8 - 7 + 3 ) x 6
( 2 + 8 ) x 3 - 6
( 4 + 8 ) / 3 x 6
6 x 8 x 3 / 6
7 + 8 + 3 + 6
( 8 / 8 + 3 ) x 6
( 9 - 8 + 3 ) x 6
( 1 + 9 ) x 3 - 6
( 3 + 9 ) / 3 x 6
3 x 9 + 3 - 6
6 + 9 + 3 + 6
6 x 9 / 3 + 6
( 9 / 9 + 3 ) x 6
( 1 - 1 + 4 ) x 6
1 x 1 x 4 x 6
1 / 1 x 4 x 6
( 2 - 1 ) x 4 x 6
( 7 + 1 - 4 ) x 6
( 8 x 1 - 4 ) x 6
( 8 / 1 - 4 ) x 6
( 9 - 1 - 4 ) x 6
( 2 - 2 + 4 ) x 6
2 / 2 x 4 x 6
( 3 - 2 ) x 4 x 6
( 4 x 2 - 4 ) x 6
( 6 + 2 - 4 ) x 6
7 x 2 + 4 + 6
8 x 2 / 4 x 6
9 / 2 x 4 + 6
( 3 - 3 + 4 ) x 6
3 / 3 x 4 x 6
( 4 - 3 ) x 4 x 6
( 5 + 3 - 4 ) x 6
( 2 x 4 - 4 ) x 6
( 4 + 4 - 4 ) x 6
( 4 - 4 + 4 ) x 6
4 x 4 / 4 x 6
4 / 4 x 4 x 6
( 5 - 4 ) x 4 x 6
9 x 4 x 4 / 6
( 3 + 5 - 4 ) x 6
( 5 - 5 + 4 ) x 6
5 / 5 x 4 x 6
( 6 - 5 ) x 4 x 6
9 + 5 + 4 + 6
( 2 + 6 - 4 ) x 6
( 6 - 6 + 4 ) x 6
6 x 6 x 4 / 6
6 / 6 x 4 x 6
( 7 - 6 ) x 4 x 6
8 + 6 + 4 + 6
( 1 + 7 - 4 ) x 6
2 x 7 + 4 + 6
7 + 7 + 4 + 6
( 7 - 7 + 4 ) x 6
7 / 7 x 4 x 6
( 8 - 7 ) x 4 x 6
( 9 + 7 ) / 4 x 6
( 1 x 8 - 4 ) x 6
2 x 8 / 4 x 6
6 + 8 + 4 + 6
( 8 + 8 ) / 4 x 6
( 8 - 8 + 4 ) x 6
8 / 8 x 4 x 6
( 9 - 8 ) x 4 x 6
9 x 8 / 4 + 6
4 x 9 x 4 / 6
5 + 9 + 4 + 6
( 7 + 9 ) / 4 x 6
8 x 9 / 4 + 6
( 9 - 9 + 4 ) x 6
9 / 9 x 4 x 6
( 5 + 1 ) x 5 - 6
6 x 1 x 5 - 6
6 / 1 x 5 - 6
( 7 - 1 ) x 5 - 6
( 8 + 1 - 5 ) x 6
( 9 x 1 - 5 ) x 6
( 9 / 1 - 5 ) x 6
( 1 - 2 + 5 ) x 6
3 x 2 x 5 - 6
( 4 + 2 ) x 5 - 6
( 7 + 2 - 5 ) x 6
( 8 - 2 ) x 5 - 6
( 2 - 3 + 5 ) x 6
2 x 3 x 5 - 6
( 3 + 3 ) x 5 - 6
( 3 x 3 - 5 ) x 6
( 6 + 3 - 5 ) x 6
( 9 - 3 ) x 5 - 6
( 2 + 4 ) x 5 - 6
( 3 - 4 + 5 ) x 6
( 5 + 4 - 5 ) x 6
5 x 4 / 5 x 6
9 + 4 + 5 + 6
( 1 + 5 ) x 5 - 6
( 4 + 5 - 5 ) x 6
( 4 - 5 + 5 ) x 6
4 x 5 / 5 x 6
4 / 5 x 5 x 6
5 x 5 + 5 - 6
7 x 5 - 5 - 6
8 + 5 + 5 + 6
1 x 6 x 5 - 6
( 3 + 6 - 5 ) x 6
( 5 - 6 + 5 ) x 6
7 + 6 + 5 + 6
( 2 + 7 - 5 ) x 6
5 x 7 - 5 - 6
6 + 7 + 5 + 6
( 6 - 7 + 5 ) x 6
( 1 + 8 - 5 ) x 6
5 + 8 + 5 + 6
( 7 - 8 + 5 ) x 6
( 1 x 9 - 5 ) x 6
4 + 9 + 5 + 6
( 8 - 9 + 5 ) x 6
( 2 + 1 ) x 6 + 6
3 x 1 x 6 + 6
3 / 1 x 6 + 6
( 4 + 1 ) x 6 - 6
( 4 - 1 ) x 6 + 6
5 x 1 x 6 - 6
5 / 1 x 6 - 6
( 6 - 1 ) x 6 - 6
( 9 + 1 - 6 ) x 6
( 1 + 2 ) x 6 + 6
( 3 + 2 ) x 6 - 6
( 5 - 2 ) x 6 + 6
( 5 x 2 - 6 ) x 6
6 x 2 + 6 + 6
6 / 2 x 6 + 6
(