Futoshiki

Hard Futoshiki uses a 6×6 grid with digits 1 through 6 and a denser network of inequality constraints. The jump from 5×5 to 6×6 adds 11 more cells and significantly more candidate combinations.

Inequality chain reasoning is key at this level. Follow sequences of connected inequalities: if A < B < C, then A ≤ 4, B is between 2 and 5, and C ≥ 3. Longer chains narrow candidates aggressively and often force placements that aren't obvious from single constraints alone.

Hard puzzles are solvable without guessing. If you feel stuck, trace the inequality chains from cells you've already filled. There's usually a propagation you haven't fully exploited.