Problem 93

Given a list of integer numbers, find a correct way of inserting arithmetic signs (operators) such that the result is a correct equation.

Example: With the list of numbers [2,3,5,7,11] we can form the equations 2-3+5+7 = 11 or 2 = (3*5+7)/11 and ten others.

Division should be interpreted as operating on rationals, and division by zero should be avoided.

[2,3,5,7,11]

2 = 3-(5+7-11)
2 = 3-5-(7-11)
2 = 3-(5+7)+11
2 = 3-5-7+11
2 = (3*5+7)/11
2*(3-5) = 7-11
2-(3-(5+7)) = 11
2-(3-5-7) = 11
2-(3-5)+7 = 11
2-3+5+7 = 11