Verbal Arithmetic Puzzle

Solve verbal arithmetic column by column from right to left, not by assigning every letter blindly. Keep a map letter-to-digit, a used-digit set, and carry. At a column, sum assigned addend digits plus carry; if one letter remains unassigned, its required result digit is forced modulo ten, which is strong pruning. If several letters are unassigned, try unused digits, never assigning zero to a leading letter of a multi-character word. Recurse to the next column only when the result digit and new carry match. The worst case remains exponential, bounded by permutations of at most ten digits, but column validation cuts most branches. Test a single-word result, final carry, repeated letters in a column, and unsatisfiable leading-zero cases. Explain the state and restore assignments exactly on backtrack.

Complexity: With at most 10 distinct letters and L total character positions, backtracking has O(10! * L) worst-case time and O(10 + L) auxiliary space.