I need help with a logical thing. Suppose I have an equation with multiple numbers (which are all single digits and 1-9).
For example: $4 * 4 - 3 = 13.$ How can I proof, that this equation has only one solution when the operators are unknown?
I want to generate puzzles in the form 4 ◦ 7 ◦ 1 ◦ 9 ◦ 8 ◦ 1 ◦ 8 ◦ 2 ◦ 2 = 134 where each ◦ represents a unknown operator. But each puzzle must have a definite solution, meaning it can only be solved in one way.
For example: $3\ ?\ 4\ ?\ 3 = 15$
Has the solutions: $3 * 4 + 3 = 15$ and $3 + 4 * 3 = 15$ (Which is not something I want to have.)
Maybe the reverse polish notation helps? When generating using trees to compare it somehow? My current solution is to brute-force all possible solutions and check if the outcome has multiple ways of solving.