Cryptic Math Equation (Backtracking)
Explore how to solve a cryptic math equation by assigning unique digits to letters using backtracking. Learn to implement a recursive algorithm in Ruby that efficiently checks combinations and enforces puzzle constraints to find valid solutions.
Problem
We want to solve this cryptic equation. Each letter stands for a unique digit (0–9). There are no leading zeros. Write a program that finds a numeric assignment to the letters for which the given equation is satisfied.
UKUSA+ USSR--------AGING
Purpose
Backtracking to solve number puzzles
Analyze
The brute-force approach by nesting loops will work for this puzzle, but won’t be elegant. We could use backtracking to solve this puzzle instead.
We have 8 letters here—U, K, S, A, R, G, I, and N.
For each letter, possible values are 0–9. So, our backtracking algorithm can be as follows:
Starting with the first letter U, ...