Let's walk through the classic puzzle.

1. Identify unique letters: S, E, N, D, M, O, R, Y — 8 letters.
2. Leading letters: S and M cannot be 0.
3. Column analysis (rightmost first):
   • D + E = Y (+ possible carry)
   • N + R (+ carry) = E (+ carry × 10)
   • E + O (+ carry) = N (+ carry × 10)
   • S + M (+ carry) = MO (two digits → M must be 1)
4. Deduction: Since MONEY is 5 digits and SEND/MORE are 4, M = 1 and S ≥ 8. With constraints, S = 9.
5. Continue back-substituting to get O = 0, E = 5, N = 6, D = 7, R = 8, Y = 2.

Backtracking is a Depth-First Search (DFS) strategy that builds candidates incrementally and abandons a branch as soon as it detects the partial solution is invalid.

function solve(charIndex) {
  if (charIndex === chars.length) {
    return evaluate();      // check if sum == 0
  }
  for (digit = 0 to 9) {
    if (digit not used AND passes constraints) {
      assign(chars[charIndex], digit);
      if (solve(charIndex + 1)) return true;
      unassign(chars[charIndex]);
    }
  }
  return false;             // backtrack
}

Pruning optimizations:

• Leading-zero skip — skip digit 0 for first letters.
• Weight-based evaluation — convert words to character weights (base-10 positions), check weighted sum equals zero instead of evaluating full words each time.

• Constraint Satisfaction Problems (CSP) — Foundation for AI planning and scheduling.
• Cryptography — Understanding substitution cipher techniques.
• Education — Teaching logical/mathematical reasoning in schools.
• Competitive Programming — Common puzzle type in coding contests.
• Game Design — Puzzle games based on alphametic concepts.