# How to find the the relationship between different numbers

Assuming i have 4 numbers a,b,c and d, my question is how can i find the right set(s) of operands a,b,c,d and operators which gives a specific result d, for example to find the right expression containing the operands 1,2,3 and 4 which evaluate to 24, a possible solution would be: 1*2*3*4 = 24 or 2*3*4/1 = 24, is there a tool/method to do this?.

You could e.g. see though, that it's difficult to construct $\pi$ with natural numbers, as $\pi$ is transcendental. So you will need more than just the standard operators.
• Sure, we could do some coding but a program is just an algorithm that a computer can understand. As I've explained, numbers as $\pi$ need more than standard operators. That'd already be a problem. – Qi Zhu Oct 22 '17 at 19:40
I personal didn't get your question well you need four numbers $A$ $B$ $C$ $D$, which on a particular operations gives a result $d$, Find all possible expression by which the variables $A$, $B$, $C$, and $D$ can be manipulated by an operation to give the same result $d$. If there was no repetition of any of the variable, we would not be able to get anything new $1×2×3×4 = 24$ and $(2×3×4) \div 1 = 24$.
$1$, $2$, $3$and $4$ Worked without repetition because one of the the variable there was equal to $1$, multiplying and dividing by $1$ is same. so there must be repetition of this variables if-not, we wouldn't get anything. Now let's first assume the product of all the variables was $d$ $$A × B × C × D = d$$ finding another operation by which we can manipulate $A$ $B$ $C$ $D$ depends on the actual value of these variables.. If we were forced to to repeat a variable, then $$\cdot A \cdot B \cdot C \cdot D \lt d$$ because introducing other maths operation like $+$ $-$ and $÷$, would lesser its value Now without repetition there are infinite ways to make up these, just by mixing and repeating the numbers