What is Futoshiki?
Futoshiki is a Latin square puzzle: put the numbers 1 to N once in every row and column of an N×N grid, while also respecting the inequality signs (<, >) printed between cells. The name is Japanese for "inequality", and the puzzle is also known as More or Less.
Unlike ordinary sudoku there are no 3×3 boxes. The signs do that job instead: the open side of a sign faces the bigger number, so "3 > □" means the box holds 1 or 2. There are only a few given numbers, and you narrow each cell down by combining the digits you know with the signs around it.
What are the exact rules?
There are only three. No repeated number in a row, no repeated number in a column, and every sign must point the right way. Each board has exactly one arrangement that satisfies all three.
| Rule | Meaning |
|---|---|
| Row | Each row holds 1 to N once. On a 5×5 board that is 1, 2, 3, 4, 5 |
| Column | Each column also holds 1 to N once |
| Sign | The open side of < or > faces the bigger number. Between cells above and below, the sign is drawn as ∧ or ∨ |
| Givens | Numbers in grey cells are fixed |
| Finish | All cells filled and nothing breaks the three rules |
How do I solve it?
Look first at the ends of the signs. On a 4×4 board the 1 is smaller than everything, so it can never sit on the big side of a sign, and the 4 can never sit on the small side. When signs link up into a chain, whole cells are often settled at once.
| Pattern | What it tells you (4×4) |
|---|---|
| □ > □ | The left cell is not 1 and the right cell is not 4 |
| □ < □ < □ | Left is 1 or 2, middle is 2 or 3, right is 3 or 4 |
| □ < □ < □ < □ | A chain of N-1 signs fixes the cells as 1, 2, 3, 4 |
| 4 > □ | Nothing yet. Three numbers are smaller than 4 |
| 2 > □ | The box must be 1 |
| □ < 2 | The box must be 1 |
- Start with chains of signs. Two or more linked signs cut the candidates at both ends sharply. Pencil the candidates in with memo and the rest falls into place later.
- Count what is missing from each row and column. When four cells of a row are filled, the last cell is the missing digit.
- Look for hidden singles. If a digit fits only one cell of a row, that cell takes it even when other candidates are pencilled there.
- Stuck? Press Check. Cells and signs that break a rule turn red. Hint fills one cell that can be deduced from the current board.
How do the sizes differ?
4×4 is a warm up you finish inside a minute, 5×5 is the classic size, and 6×6 and 7×7 are for experts who pencil in candidates. Bigger boards get a few more givens and more signs.
| Size | Givens | Signs | Target time |
|---|---|---|---|
| Easy 4×4 | 0 to 3 | 4 to 6 | Under a minute |
| Normal 5×5 | 1 to 5 | 6 to 10 | About 3 minutes |
| Hard 6×6 | 2 to 7 | 8 to 12 | About 6 minutes |
| Expert 7×7 | 6 to 12 | 10 to 15 | 10 minutes or more |
Every board can be finished by pure deduction. You never have to guess and hope.
How are the boards made?
The game shuffles a random Latin square, picks signs between neighbouring cells, then removes the given numbers one at a time. A given stays removed only if the board can still be solved by deduction; otherwise it goes back. Signs are thinned the same way, and finally a solver confirms there is exactly one answer.
That is why boards of the same size have different numbers of givens: only the clues that are really needed remain. The share link carries the board number, so a friend who opens it gets the very same board to race on.
What is the daily puzzle?
The daily puzzle is a 5×5 board that changes every day and is the same for everyone on that day. It rolls over at midnight Korean time, and finishing it is recorded on your attendance streak.
Best times are stored separately for each size. If you leave in the middle of a board, the Continue button brings you back to the same spot.
Controls
- Phone and mouse: tap a cell to select it (blue outline), then tap a number button below the board (to the right in landscape). Tapping the same number again erases it. With Memo on, numbers are pencilled in small as candidates.
- Keyboard: digits 1 to N enter, Backspace, Delete or 0 erase, arrow keys move, N toggles memo, H hint, Z undo, C check.
- Buttons: Undo steps back through your entries one at a time. Hints used are shown with your result.
Records and unfinished boards are kept only in this browser and never sent to a server. Clearing browser data clears them too.