How to play Futoshiki

Fill a Latin square so each row and column holds 1 to N once, and every inequality sign is true. Also known as Unequal, More or Less.

▶ Play Futoshiki ⊞ Open the solver

The rules

An N×N grid uses the digits 1 to N (here 4×4 to 7×7).
Each row and each column contains each digit exactly once.
Inequality signs (< and >) between neighbouring cells must be obeyed — the sign points to the smaller number.
Some digits may be given at the start.

Playing Futoshiki on Puzzle Solvers

Choose a grid size and a difficulty, then press Generate Puzzle.
Click a cell and type a digit, or use the on-screen keypad. Notes switches to pencil marks.
Undo steps back; Force places one digit that has only one possible value; Check marks mistakes in red without giving away the answer.
Stuck? Send to Solver opens the same puzzle in the step-by-step solver. Send to Slate opens it as a board on the Slate whiteboard, to solve in front of a class.

Open the Futoshiki game →

Using the Futoshiki solver

① Build: choose the grid size, click cells to enter the given numbers, and click the gap between two cells to set the inequality sign.
② Check validates the puzzle.
③ Solve It shows every deduction in plain English, one step at a time.

Open the solver →

A worked example

In a 4×4 row the signs read A < B < C < D. Four different digits in strictly increasing order from 1–4 can only be 1, 2, 3, 4 — the row is solved by the signs alone.

In another row, only one sign says B > C. So B cannot be 1 and C cannot be 4. If the column already holds 2 and 3 for B, then B = 4.

Strategies

Ends of a chain. A cell that is greater than its neighbour can never be 1; a cell that is smaller can never be N.
Long chains. A chain of k cells each smaller than the next forces the first to be at most N−k+1 and the last at least k. A chain of 4 in a 4×4 is exactly 1, 2, 3, 4.
Singles. As in Sudoku, look for the only cell in a row or column that can take a digit.
Pencil marks. Write candidates and trim them with every sign; the signs propagate limits along rows and columns.

Common mistakes

Reading the sign backwards. The open side faces the larger number.
Forgetting the column — every digit must be unique in its column too.

Where it comes from

Futoshiki (Japanese for 'not equal') was created in Japan in 2001 and became a regular newspaper puzzle in the UK a few years later.

Frequently asked questions

Which way does the arrow point?

From the larger number to the smaller one — like the open mouth of < and >, the wide side faces the bigger number.

What sizes can I play?

The Futoshiki game generates 4×4 to 7×7 grids from Easy to Devilish.

Can the solver explain a newspaper puzzle?

Yes. Enter the givens, click between cells to set the signs, then run the Futoshiki Solver step by step.

Is Futoshiki a Latin square?

Yes — a Latin square with inequality clues added.

Keep going

All guides: How to play every puzzle and game.