About Futoshiki

Futoshiki is a Japanese logic puzzle that adds inequality constraints to a Latin square framework. The name means "not equal" in Japanese, reflecting the puzzle's core mechanic of using greater-than and less-than symbols to guide number placement. This elegant combination creates puzzles that are simultaneously approachable and deeply challenging.

How to Play Futoshiki

Fill the grid with numbers following these rules:

• Complete the grid: Every cell must contain a number from 1 to the grid size (4 for 4×4, 5 for 5×5, etc.)
• Unique rows: Each number must appear exactly once in every row
• Unique columns: Each number must appear exactly once in every column
• Respect inequalities: All greater-than (>) and less-than (<) symbols must be satisfied

Begin by identifying cells where inequalities severely constrain options, then use Latin square logic combined with inequality chains to make progress. The interaction between row/column uniqueness and inequalities creates rich solving opportunities.

Grid Sizes

Strategy Tips

• Follow inequality chains: Use sequences of inequalities to determine minimum and maximum possible values
• Identify forced cells: Find cells where inequalities and uniqueness constraints leave only one option
• Use extremes: The largest and smallest numbers in a row/column are often determined by inequality constraints
• Combine constraints: Look for cells where both row/column logic and inequalities converge to force a value

Why Play Futoshiki?

Futoshiki develops multi-constraint reasoning skills by requiring solvers to balance numerical uniqueness with relational logic. This dual-constraint system enhances cognitive flexibility and strengthens the ability to work with complex, interrelated rules. It's perfect for puzzle enthusiasts who enjoy mathematical reasoning combined with logical deduction.