Futoshiki solver

This futoshiki solver takes the puzzle in front of you: pick the size, type the numbers that are given, and set each sign between the cells. Press Solve for the whole answer, or Next step to get one number at a time with the reasoning behind it. The solver also tells you when a puzzle has more than one answer, or none.

The rules of futoshiki

A futoshiki of size 5 uses the numbers 1 to 5. Every row and every column holds each number exactly once, as in a Latin square. A sign between two neighbors must be true: in a < b the left cell is smaller, and a sign pointing up or down compares a cell with the one below it. The open side of the sign always faces the bigger number. The name is Japanese for "not equal".

How to enter a puzzle

1. Choose the size. The grid clears when you change it.
2. Tap a cell and type its number with the keyboard or the number pad.
3. Tap the gap between two cells to cycle its sign: none, smaller, bigger. On a phone it is easier to select the left or upper cell and use the sign buttons under the grid, which set the sign to its right or below it.

You can also paste the whole grid as text, for example .<. . 3 for a row and a line of ^ and v marks for the signs between two rows.

How the solver works

Each cell keeps a list of the numbers still possible. Numbers already in the same row or column are removed; a number that fits only one cell of a row or column goes there. Each sign trims both of its cells: in a < b, the cell a cannot hold the largest number b could hold or anything above it, and b cannot hold the smallest a could hold or anything below. These rules repeat until nothing changes. If cells are still open, the solver picks the cell with the fewest options, tries each one and repeats, and it carries on after the first answer to prove whether a second one exists.

The step hints use the same rules in the order a person would, starting with the simplest: a cell where only one number is left, a number with only one place in a row or column, then the signs. On the generated test puzzles, from 4 by 4 to 9 by 9, close to nine in ten steps are found by these rules alone; when none applies, the hint says so plainly.

Worked example

In a 4 by 4 grid, suppose a row reads a < b < c followed by a free fourth cell. The chain needs three different rising numbers, so a is at most 2, b is 2 or 3, and c is at least 3. If the column through c already contains a 4, then c is 3, which forces b to 2 and a to 1, and the fourth cell of the row is 4.

Solving tips

• Follow chains of signs: a chain of k cells going up means the first is at most n - k + 1 and the last at least k.
• The cell at the small end of a sign can never be the biggest number, and the cell at the big end can never be 1.
• When a row is nearly full, count: the missing numbers and the signs usually leave one way to place them.

The skyscraper puzzle and calcudoku use the same Latin square grid with other clues: building heights seen from the edge, and math cages.

Prefer to play? Our futoshiki page has new 4x4 to 6x6 grids and a daily puzzle, each checked by this solver.

Solver tested 1 October 2026. Found a problem? Tell us.

Questions