Futoshiki Generator

What is a Futoshiki Generator?

A Futoshiki generator is a puzzle creation tool that produces unique inequality logic puzzles. Futoshiki (Japanese for "inequality") challenges you to fill an NxN grid with numbers while respecting inequality signs between adjacent cells and ensuring each row and column contains unique values. This generator supports grid sizes from 4x4 to 9x9 with multiple difficulty levels, interactive solving features, and reproducible puzzles via seed sharing. Try our crossword puzzle maker and bingo card generator for other puzzle tools.

Unlike Sudoku, Futoshiki has no 3x3 box constraints. Instead, inequality signs (greater-than, less-than, and vertical comparison marks) provide the additional constraints that make each puzzle unique and challenging.

What is Futoshiki?

Futoshiki (also known as "Unequal") is a number placement puzzle originating from Japan. The puzzle consists of a square grid with inequality signs between some adjacent cells. Your goal is to fill every empty cell with a number such that:

• Latin Square Rule: Each row and each column must contain the numbers 1 through N exactly once, where N is the grid size.
• Inequality Rule: All inequality signs between cells must be satisfied. The open (wider) side of the sign always points to the larger number.

The puzzle starts with some cells pre-filled (called "givens" or "clues") and some inequality signs displayed. Your task is to deduce the remaining numbers using pure logic -- no guessing required for a well-crafted Futoshiki puzzle. You can also generate cryptogram puzzles for a different type of logic challenge.

How to Read Inequality Signs

Understanding the inequality signs correctly is essential for solving Futoshiki puzzles:

• Horizontal $>$ (greater-than): The left cell contains a larger number than the right cell. Example: 3 > 1 means the number 3 is on the left and 1 is on the right.
• Horizontal $<$ (less-than): The left cell contains a smaller number than the right cell. Example: 2 < 5 means 2 is on the left and 5 is on the right.
• Vertical $\vee$ (V-shape): The top cell is larger than the bottom cell. The V opens upward, pointing to the larger number above.
• Vertical $\wedge$ (caret/A-shape): The top cell is smaller than the bottom cell. The caret opens downward, pointing to the larger number below.

How to Solve Futoshiki Puzzles

Step 1: Start with Extremes

Look for cells that must contain the smallest (1) or largest (N) possible number. If a cell has inequality signs on both sides pointing away from it (both neighbors must be larger), that cell must contain 1. Similarly, if both signs point toward a cell (both neighbors must be smaller), that cell must contain N (the grid size).

Step 2: Chain Reasoning

Follow chains of inequality signs to constrain possible values. For example, if you see $A < B < C$ in a row of a 4x4 grid, then A can only be 1 or 2, B can be 2 or 3, and C can be 3 or 4. The length of the inequality chain directly constrains the possible values at each position.

Step 3: Latin Square Elimination

Apply standard Latin square elimination. If a row already contains the numbers 1, 3, and 5, the remaining two cells must contain 2 and 4. Combine this information with the inequality constraints to determine the exact placement of each remaining number.

Step 4: Use Pencil Marks

For harder puzzles, use pencil marks (small candidate numbers) to track possible values for uncertain cells. As you eliminate possibilities by applying row/column constraints and inequality rules, update your pencil marks. Our interactive solver includes a pencil mark mode for this purpose.

Difficulty Levels Explained

• Easy: Approximately 85% of inequality signs are shown and about 35% of cells are pre-filled. Many cells can be solved directly from the given information with minimal inference. Perfect for learning Futoshiki logic.
• Medium: Approximately 60% of signs are shown with about 20% given cells. Requires combining multiple constraints and basic Latin square elimination. The classic newspaper-style solving experience.
• Hard: Approximately 40% of signs are shown with about 10% given cells. Demands longer deduction chains and careful tracking of candidates across rows and columns.
• Expert: Only approximately 25% of signs are shown with no given numbers at all. Every digit must be deduced purely from inequality constraints and Latin square rules. A true test of logical reasoning ability.

Available Grid Sizes

• 4x4: Quick and approachable. Uses numbers 1-4. Great for beginners or a fast warm-up puzzle.
• 5x5 (Classic): The standard Futoshiki size found in newspapers and puzzle books worldwide. Uses numbers 1-5. The perfect balance of challenge and accessibility. You can also try our lottery number generator for other number-based generators.
• 6x6: A moderate step up from the classic size. More cells and constraints mean more complex interactions to track and deduce.
• 7x7: A substantial challenge requiring systematic candidate tracking and multi-step logical deductions.
• 9x9: The largest grid size available. With 81 cells and dozens of constraints, this is designed for experienced puzzle solvers seeking a deep logical workout.

Interactive Solver Features

• Click-to-Fill: Select any non-given cell and type a number using your keyboard or the on-screen numpad.
• Pencil Marks: Toggle pencil mode (press P) to add small candidate numbers inside cells, helping you track possibilities during complex deductions.
• Arrow Key Navigation: Use the up, down, left, and right arrow keys to move between cells efficiently.
• Timer: Track your solving time to measure improvement and compare with friends.
• Undo: Press Ctrl+Z or click Undo to reverse your last move.
• Check: Click Check to verify your entries against the solution and count any errors.
• Show Solution: If you get stuck, reveal the complete answer.
• Print: Generate a clean, print-friendly version for offline solving on paper.

Puzzle Seed for Sharing

Every puzzle generated by this tool can be exactly reproduced using a puzzle seed. The same combination of seed, grid size, and difficulty level always produces the identical puzzle. Share your seed with friends, classmates, or puzzle communities so everyone can solve the exact same puzzle and compare solving times. Leave the seed field empty for a completely random puzzle each time you generate.