About Futoshiki
Futoshiki fills a grid with digits 1 through N so each digit appears exactly once per row and column, same as a Latin square. Scattered between some cells are inequality signs (< or >) that must hold true between those two neighbors — that's the only extra clue you get, and it's enough to pin down a unique solution.
The Rules
Fill the grid with digits 1–N, once per row and column, so every greater-than or less-than arrow between cells is satisfied.
Step by Step
- Fill every row and column with the digits 1 through N, with no repeats.
- Some pairs of neighboring cells have a < or > sign between them, showing which one must be larger.
- Every inequality sign on the board must hold true in the finished grid.
- Some digits may be given at the start to help anchor the solution.
- The puzzle is solved when the grid is full, the Latin-square rule holds, and every inequality is satisfied.
Tips & Strategy
- A chain of inequalities in one row (like a < b < c) immediately rules out the highest values for the first cell and the lowest for the last.
- The digit 1 can never be on the larger side of an inequality, and the highest digit can never be on the smaller side — use that to eliminate options fast.
- Combine inequality clues with the row/column uniqueness rule — a digit ruled out by one often narrows the other.
- Work outward from cells with the most inequality signs attached — they're the most constrained.
Frequently Asked Questions
Do all cells start with an inequality sign?
No — only some neighboring pairs have a < or > between them. The rest of the solving comes from the standard Latin-square (no repeats per row/column) rule.
Is Futoshiki related to Sudoku?
They share the Latin-square core (no repeated digit per row or column), but Futoshiki replaces Sudoku's box rule with inequality clues between cells.
Is there always exactly one solution?
Yes — every generated Futoshiki puzzle has one unique solution reachable through logical deduction alone.
