Futoshiki Puzzles
Fill the grid so each row and column holds every number once, and every greater-than sign points from the larger number to the smaller. Every puzzle here is checked before you see it: exactly one solution, and always solvable by reasoning alone.
Also known as unequal, more or less and inequality sudoku. The name is Japanese for “not equal”.
Related Practice
What Is Futoshiki?
Futoshiki is a Japanese logic puzzle played on a small square grid. You fill it so that every row and every column contains each number from 1 up to the grid size exactly once — that part is a Latin square, the same rule that underpins sudoku. What makes it futoshiki is the inequality signs printed between some pairs of neighbouring cells: each one must point from the larger number to the smaller when the grid is finished.
The name is Japanese for “not equal”. A puzzle usually starts with only a handful of numbers given, sometimes none at all, so nearly everything comes from the signs and from the Latin square rule working against each other.
How To Solve A Futoshiki
There is a dependable order, and it starts with the signs rather than the numbers. A greater-than sign is easiest to use as an elimination, not as a comparison.
- Read what each sign forbids. If A is greater than B, then A cannot be 1 and B cannot be the largest number in the grid. On a 5×5 that removes two candidates immediately, before you have thought about anything else.
- Follow the chains. Where signs run in a line — A greater than B greater than C — the whole run is forced. Three rising cells on a 5×5 mean the lowest is at most 3 and the highest at least 3, which often settles a cell outright.
- Apply the Latin square rule. Every number placed can be struck from the rest of its row and its column. This is the bookkeeping that turns constrained cells into decided ones.
- Look for the only home. If a number can go in just one cell of a row, it goes there, even if that cell still has other candidates. People miss this far more often than they miss a cell with one candidate left.
Every Futoshiki Here Is Solvable By Pure Logic
This is the part worth being precise about, because most sites cannot say it. Every puzzle on this page passes two machine checks before it is shown to you.
| Guarantee | How it is checked | What happens if it fails |
|---|---|---|
| Exactly one solution | A backtracking solver counts solutions and stops at two. | The puzzle is discarded and a different one generated. |
| No guessing required | A second solver, allowed only human techniques, must finish it unaided. | Same — discarded, never shown. |
The second solver is also what powers Show me the next move. Rather than filling in the grid, it replays the single next deduction it made and tells you the reason — which cell, which number, and which sign or row forced it. You can take one step, then go back to solving. That is the opposite of a solve button, and it is deliberate.
The Sizes Here, And What Changes Between Them
| Size | Candidates per cell | What it asks of you |
|---|---|---|
| 4×4 | 4 | Holdable in your head. The right place to learn what a sign rules out. |
| 5×5 | 5 | The standard size. Enough room for chains to matter. |
| 6×6 | 6 | Pencil marks stop being optional; tracking becomes part of the puzzle. |
| 7×7 | 7 | Signs carry the most weight here — one comparison removes a lot at once. |
Futoshiki Puzzles Frequently Asked Questions
What is futoshiki?
A Japanese logic puzzle played on a square grid. You fill it so that every row and every column contains each number from 1 to the grid size exactly once — a Latin square — while satisfying inequality signs printed between some pairs of neighbouring cells. The name means "not equal". A few numbers may be given to start; the rest come from the signs and the Latin square rule.
Does every futoshiki have only one solution?
A well-made one does, but a hand-drawn grid with too few signs or givens can easily have several. Every puzzle on this page is machine-checked before it is shown: a solver counts the solutions and the puzzle is discarded unless there is exactly one. That check is why the grids here sometimes carry a given you might not expect.
What does the futoshiki inequality sign mean?
It points at the smaller number. A sign between two cells reading A greater than B means whatever goes in A must be larger than whatever goes in B. Signs only ever appear between cells that touch side by side or one above the other, never diagonally, and a cell can carry several signs on different edges.
Can futoshiki be solved without guessing?
Every puzzle here can, and that is verified rather than assumed. Before a puzzle is shown, a solver that uses only human techniques — candidate elimination, inequality bounds, and the only-place-it-can-go rule — must complete it unaided. If it cannot, the puzzle is thrown away and a different one is generated.
What size futoshiki should I start with?
Start at 4×4, where each cell has only four candidates and you can hold the whole grid in your head. Move to 5×5 once the inequality reasoning feels automatic; that is the size most published futoshiki use. The 6×6 and 7×7 grids here are a genuine step up, because more candidates per cell means pencil marks stop being optional.
Is futoshiki the same as sudoku?
They share the idea that each number appears once per row and column, but futoshiki has no boxes and adds the inequality signs, which sudoku has nothing like. Futoshiki grids are also much smaller — typically 5×5 rather than 9×9 — so the reasoning is denser rather than longer.
How do you solve a futoshiki puzzle?
Start where the signs stack up rather than where the numbers are. A run of two signs pointing the same way fixes its ends — in a 5×5, a cell at the open end of two consecutive greater-than signs cannot be lower than 3. After that it is ordinary Latin-square work: each number once per row and column, so eliminate along lines and let the signs settle the ties.