Sudoku

The board is a 9×9 array of numbers (0 = empty). Immutable updates ensure React re-renders correctly without mutating state.

Checks a candidate value against its row, column, and 3×3 box simultaneously. Used during both puzzle generation and the hint solver.

Fills a blank grid with a valid solution via shuffled backtracking, then removes cells while checking uniqueness (countSolutions ≤ 1). Difficulty controls how many clues remain: Easy ≈ 46, Medium ≈ 32, Hard ≈ 24.

The hint system uses constraint propagation + bounded backtracking. Depth 1 finds naked singles (only one legal value). Higher depths apply the MRV heuristic and try candidates to eliminate contradictions - revealing cells that require deeper logical inference.

Difficulty is purely a function of how many clues are left in the puzzle. Fewer clues means more cells need to be deduced, which typically requires deeper search techniques.