What Is Futoshiki?
Futoshiki is a Latin-square logic puzzle, sometimes described as an unequal puzzle or inequality puzzle. Fill an N×N grid with the numbers 1 through N so that no number repeats in any row or column.
The inequality signs between selected neighboring cells add the defining constraint. They establish which number must be larger, turning each sign into a useful bound, comparison, or link in a longer deduction chain.
How to Play Futoshiki
Use row and column elimination together with every inequality. Candidate notes help when a cell still has several possible values.
- Fill every cell with a number from 1 to the board size.
- Use each number exactly once in every row.
- Use each number exactly once in every column.
- Make every neighboring pair agree with its inequality sign.
How the Inequality Signs Work
The open side of an inequality faces the larger number, while its narrow point faces the smaller number. A horizontal A < B sign means the left value is smaller. On a vertical sign, the wedge points toward the smaller of the top and bottom cells.
Futoshiki Strategies
- Start with rows and columns that already contain several given numbers, then list the missing values.
- Use immediate bounds: the smaller side of an inequality cannot be the largest number, and the larger side cannot be 1.
- Follow inequality chains. A three-cell increasing chain needs three ordered values, which sharply limits both endpoints.
- Combine candidate notes with row and column uniqueness instead of treating each inequality in isolation.
- When a candidate has no supporting value on the other side of an inequality, remove it even if neither cell is solved yet.
Daily Futoshiki
The dated challenge uses a stable date seed, so every player receives the same reproducible puzzle. Daily progress is saved separately from unlimited games.
Play Daily FutoshikiUniquely Solvable Puzzles
Every published board is checked by a constraint solver that enforces row uniqueness, column uniqueness, givens, and every inequality. A puzzle is accepted only when the solver finds exactly one solution.
Futoshiki, Sudoku, and Calcudoku
Unlike classic Sudoku, Futoshiki has no 3×3 boxes. It shares the row-and-column Latin-square structure of Calcudoku, but replaces arithmetic cages with direct inequalities between neighboring cells.
Frequently Asked Questions
What is Futoshiki?
Futoshiki is a number logic puzzle played on a square grid. Fill each row and column with the numbers 1 through N without repeats, while satisfying every inequality between neighboring cells.
How do you play Futoshiki?
Use the given numbers, missing values in each row and column, and the inequality signs to narrow each cell's candidates. The puzzle is complete when every cell is filled and all three rule types are satisfied.
What do the inequality signs mean?
The open side faces the larger value and the narrow point faces the smaller value. Each sign compares only the two cells immediately beside it.
Can a number repeat in a row?
No. Every row contains each number from 1 through the board size exactly once.
Can a number repeat in a column?
No. Every column also contains each available number exactly once.
Does Futoshiki use Sudoku boxes?
No. There are no standard 3×3 box constraints; only row uniqueness, column uniqueness, and the displayed inequalities apply.
Does every Futoshiki puzzle have one solution?
Yes. Published puzzles are tested with a solver that stops after finding a second solution, and only boards with exactly one solution are accepted.
What size should beginners play?
A 4×4 Easy puzzle is the clearest introduction. Move to the default 5×5 format once row, column, and inequality deductions feel comfortable.
Is Futoshiki the same as Sudoku?
Both prohibit repeated numbers in rows and columns, but Futoshiki uses an N×N Latin square without Sudoku boxes and adds inequalities between adjacent cells.
Can I play Futoshiki on mobile?
Yes. The board, inequality signs, candidate notes, and number pad adapt to phone and tablet screens from 4×4 through 7×7.
Is Futoshiki free?
Yes. Unlimited and Daily Futoshiki puzzles are free to play in your browser, with no download required.
What are candidate notes?
Candidate notes are small optional numbers you can record in an unsolved cell. They help track values that remain possible after row, column, and inequality deductions.