How do you play Futoshiki?

Fill an N × N board so every row and every column holds each digit from 1 to N exactly once, like a small Sudoku without boxes. Given digits cannot change. A sign between two adjacent cells points at the smaller digit: means it is larger, ∧ between rows means the upper digit is smaller and ∨ means it is larger. On a 4 × 4 board the row 1, 2, 3, 4 is valid and 1, 2, 2, 4 is not, because 2 repeats. If a sign reads left < right and you enter 3 then 2, the board flags it, because 3 < 2 is false.

Does every puzzle have exactly one solution?

Yes. For each seed the generator fills a random Latin square, keeps a fixed number of its digits as givens (2, 5, 6 or 8 for sizes 4 to 7) and starts with a sign on every adjacent pair. It then removes signs in a seeded order, keeping a removal only when its solver still finds exactly one solution, until a quarter of the adjacent pairs keep a sign or no further sign can go. Two proofs then decide whether the puzzle is offered, and neither is given the intended answer. The first reruns the generator's solver, which narrows candidate digits using the signs, within 50,000 steps. The second is a separately written solver that tries digits cell by cell, checking each row, column and neighbouring sign directly, within 500,000 steps. Both must finish and each must find exactly one solution, the same one, and the page repeats both proofs when the puzzle opens. A candidate whose givens and signs allow two solutions is discarded, and a proof that reaches its step limit offers nothing: Generate from seed keeps the previous puzzle, and New puzzle moves on to another seed. Each seed may try up to 64 candidate grids within 60,000 steps. Steps are counted, not timed, so the same seed builds the same puzzle on every device.

How do pencil notes, hints and undo work?

Turn on Pencil notes, or press N, to mark candidate digits in a blank cell. Notes never count as submissions, and entering a digit replaces them. Fill one cell writes the correct digit into the selected cell when it is blank or wrong, otherwise into the first blank or wrong cell, and turns the run into assisted practice. Reveal solution shows the answer while keeping your own entries underneath. Undo and redo step through digit and note changes until the puzzle is solved; once every rule holds the result is final, and Replay as practice starts the same puzzle again.

How is the Futoshiki challenge scored?

The challenge is one seeded original 5 × 5 puzzle with 5 given digits. Score is 1000 minus your final retained digit submissions, never below 0, and higher is better. Each of the 20 blank cells needs at least one submission, so 980 is the best possible score. Pencil notes, erasing and re-entering an unchanged digit add nothing, and undo removes the undone submission. Fill one cell, Reveal solution, an answer key printed before finishing, restored progress, replays and puzzles already opened in this browser, including rotated, reflected or digit-reversed versions, stay practice. Scores are self-reported.

What happens when someone opens a challenge link?

The page shows the shared score, the fixed rules and a Start same challenge button; nothing starts on its own. The link carries only the seed, the board size setting and the claimed score, never digits, notes or the answer, and the board is regenerated from the seed. A link with a fractional, out-of-range, duplicated or wrong-tool value is refused with a message, and ordinary practice opens instead. After a fresh unassisted solve you see both scores, the signed difference and whether you did better, tied or scored lower, with Copy challenge link, Share challenge and Download result card for a new link that carries your score for the same puzzle.

Can I print a puzzle or come back to it later?

Print puzzle prints the given digits and signs only, without your entries, notes or the solution. Print puzzle and answer key adds the answer on a separate page and, if you have not finished, turns the run into assisted practice. Once you make a change, progress is saved in this browser without the solution. On your next visit an unfinished puzzle reopens automatically, unless you arrive through a challenge link: it is regenerated from its seed and your history is replayed onto it, as practice. Saves keep up to 10,000 changes and remember up to 1,024 opened puzzles. If storage is unavailable, the puzzle stays playable in the open tab.

Can I play with a keyboard or on a phone?

Yes. Tap a cell or use the arrow keys, then press a digit key from 1 up to the board size to enter it, Backspace or Delete to clear, and the N key to switch pencil notes. The digit pad, move buttons and a selected-cell list give the same control without a keyboard, and on narrow screens every cell and button is at least 44 pixels. Each cell's accessible name includes its digit, notes and the signs beside it, and the page lists every sign with whether it holds, plus a text version of the board.

Futoshiki Puzzles

Q: Does every puzzle have exactly one solution?

Yes. For each seed the generator fills a random Latin square, keeps a fixed number of its digits as givens (2, 5, 6 or 8 for sizes 4 to 7) and starts with a sign on every adjacent pair. It then removes signs in a seeded order, keeping a removal only when its solver still finds exactly one solution, until a quarter of the adjacent pairs keep a sign or no further sign can go. Two proofs then decide whether the puzzle is offered, and neither is given the intended answer. The first reruns the generator's solver, which narrows candidate digits using the signs, within 50,000 steps. The second is a separately written solver that tries digits cell by cell, checking each row, column and neighbouring sign directly, within 500,000 steps. Both must finish and each must find exactly one solution, the same one, and the page repeats both proofs when the puzzle opens. A candidate whose givens and signs allow two solutions is discarded, and a proof that reaches its step limit offers nothing: Generate from seed keeps the previous puzzle, and New puzzle moves on to another seed. Each seed may try up to 64 candidate grids within 60,000 steps. Steps are counted, not timed, so the same seed builds the same puzzle on every device.

Q: How do pencil notes, hints and undo work?

Turn on Pencil notes, or press N, to mark candidate digits in a blank cell. Notes never count as submissions, and entering a digit replaces them. Fill one cell writes the correct digit into the selected cell when it is blank or wrong, otherwise into the first blank or wrong cell, and turns the run into assisted practice. Reveal solution shows the answer while keeping your own entries underneath. Undo and redo step through digit and note changes until the puzzle is solved; once every rule holds the result is final, and Replay as practice starts the same puzzle again.

Q: How is the Futoshiki challenge scored?

The challenge is one seeded original 5 × 5 puzzle with 5 given digits. Score is 1000 minus your final retained digit submissions, never below 0, and higher is better. Each of the 20 blank cells needs at least one submission, so 980 is the best possible score. Pencil notes, erasing and re-entering an unchanged digit add nothing, and undo removes the undone submission. Fill one cell, Reveal solution, an answer key printed before finishing, restored progress, replays and puzzles already opened in this browser, including rotated, reflected or digit-reversed versions, stay practice. Scores are self-reported.

Q: What happens when someone opens a challenge link?

The page shows the shared score, the fixed rules and a Start same challenge button; nothing starts on its own. The link carries only the seed, the board size setting and the claimed score, never digits, notes or the answer, and the board is regenerated from the seed. A link with a fractional, out-of-range, duplicated or wrong-tool value is refused with a message, and ordinary practice opens instead. After a fresh unassisted solve you see both scores, the signed difference and whether you did better, tied or scored lower, with Copy challenge link, Share challenge and Download result card for a new link that carries your score for the same puzzle.

Q: Can I print a puzzle or come back to it later?

Print puzzle prints the given digits and signs only, without your entries, notes or the solution. Print puzzle and answer key adds the answer on a separate page and, if you have not finished, turns the run into assisted practice. Once you make a change, progress is saved in this browser without the solution. On your next visit an unfinished puzzle reopens automatically, unless you arrive through a challenge link: it is regenerated from its seed and your history is replayed onto it, as practice. Saves keep up to 10,000 changes and remember up to 1,024 opened puzzles. If storage is unavailable, the puzzle stays playable in the open tab.

Q: Can I play with a keyboard or on a phone?

Yes. Tap a cell or use the arrow keys, then press a digit key from 1 up to the board size to enter it, Backspace or Delete to clear, and the N key to switch pencil notes. The digit pad, move buttons and a selected-cell list give the same control without a keyboard, and on narrow screens every cell and button is at least 44 pixels. Each cell's accessible name includes its digit, notes and the signs beside it, and the page lists every sign with whether it holds, plus a text version of the board.

Futoshiki is a Latin square puzzle with inequality signs: every row and column of an N × N board holds 1 to N once, and every sign between adjacent cells must hold. Each puzzle here is original, generated on this page from a seed in sizes 4 × 4 to 7 × 7, and offered only after a solver proves it has exactly one solution. Enter digits or pencil notes by tap or keyboard, undo and redo, and see repeated digits and broken signs flagged from the rules alone. Fill one cell and Reveal solution are there when you want help, progress is saved in this browser, and you can print the puzzle with a separate answer key only when you ask for one. Solve a fresh 5 × 5 puzzle without help and you can send the same puzzle as a scored challenge.

Fill the board so every row and column holds each digit once. A sign between two cells points at the smaller digit, and every sign must hold.

Your puzzleBoard sizes 4 × 4 to 7 × 7

Board sizeSeed

The inequality rule
A sign points at the smaller cell: 2 < 4 holds and 3 < 2 does not. Between rows, ∧ means the upper digit is smaller and ∨ means it is larger.

Original Futoshiki boardWaiting for a puzzle

Building a puzzle
A new puzzle appears once a solver has proved it has exactly one solution.

Preparing an original Futoshiki puzzle.

1, 2, 3, 4Row on a 4 × 4 boardValid: each digit from 1 to 4 appears once.
1, 2, 2, 4Row on a 4 × 4 boardInvalid: 2 appears twice.
3 < 2Left cell < right cellRejected: 3 < 2 is false, so a conflict is shown.

Common questions

How do you play Futoshiki?: Fill an N × N board so every row and every column holds each digit from 1 to N exactly once, like a small Sudoku without boxes. Given digits cannot change. A sign between two adjacent cells points at the smaller digit: < means the left digit is smaller, > means it is larger, ∧ between rows means the upper digit is smaller and ∨ means it is larger. On a 4 × 4 board the row 1, 2, 3, 4 is valid and 1, 2, 2, 4 is not, because 2 repeats. If a sign reads left < right and you enter 3 then 2, the board flags it, because 3 < 2 is false.
Does every puzzle have exactly one solution?: Yes. For each seed the generator fills a random Latin square, keeps a fixed number of its digits as givens (2, 5, 6 or 8 for sizes 4 to 7) and starts with a sign on every adjacent pair. It then removes signs in a seeded order, keeping a removal only when its solver still finds exactly one solution, until a quarter of the adjacent pairs keep a sign or no further sign can go. Two proofs then decide whether the puzzle is offered, and neither is given the intended answer. The first reruns the generator's solver, which narrows candidate digits using the signs, within 50,000 steps. The second is a separately written solver that tries digits cell by cell, checking each row, column and neighbouring sign directly, within 500,000 steps. Both must finish and each must find exactly one solution, the same one, and the page repeats both proofs when the puzzle opens. A candidate whose givens and signs allow two solutions is discarded, and a proof that reaches its step limit offers nothing: Generate from seed keeps the previous puzzle, and New puzzle moves on to another seed. Each seed may try up to 64 candidate grids within 60,000 steps. Steps are counted, not timed, so the same seed builds the same puzzle on every device.
How do pencil notes, hints and undo work?: Turn on Pencil notes, or press N, to mark candidate digits in a blank cell. Notes never count as submissions, and entering a digit replaces them. Fill one cell writes the correct digit into the selected cell when it is blank or wrong, otherwise into the first blank or wrong cell, and turns the run into assisted practice. Reveal solution shows the answer while keeping your own entries underneath. Undo and redo step through digit and note changes until the puzzle is solved; once every rule holds the result is final, and Replay as practice starts the same puzzle again.
How is the Futoshiki challenge scored?: The challenge is one seeded original 5 × 5 puzzle with 5 given digits. Score is 1000 minus your final retained digit submissions, never below 0, and higher is better. Each of the 20 blank cells needs at least one submission, so 980 is the best possible score. Pencil notes, erasing and re-entering an unchanged digit add nothing, and undo removes the undone submission. Fill one cell, Reveal solution, an answer key printed before finishing, restored progress, replays and puzzles already opened in this browser, including rotated, reflected or digit-reversed versions, stay practice. Scores are self-reported.
What happens when someone opens a challenge link?: The page shows the shared score, the fixed rules and a Start same challenge button; nothing starts on its own. The link carries only the seed, the board size setting and the claimed score, never digits, notes or the answer, and the board is regenerated from the seed. A link with a fractional, out-of-range, duplicated or wrong-tool value is refused with a message, and ordinary practice opens instead. After a fresh unassisted solve you see both scores, the signed difference and whether you did better, tied or scored lower, with Copy challenge link, Share challenge and Download result card for a new link that carries your score for the same puzzle.
Can I print a puzzle or come back to it later?: Print puzzle prints the given digits and signs only, without your entries, notes or the solution. Print puzzle and answer key adds the answer on a separate page and, if you have not finished, turns the run into assisted practice. Once you make a change, progress is saved in this browser without the solution. On your next visit an unfinished puzzle reopens automatically, unless you arrive through a challenge link: it is regenerated from its seed and your history is replayed onto it, as practice. Saves keep up to 10,000 changes and remember up to 1,024 opened puzzles. If storage is unavailable, the puzzle stays playable in the open tab.
Can I play with a keyboard or on a phone?: Yes. Tap a cell or use the arrow keys, then press a digit key from 1 up to the board size to enter it, Backspace or Delete to clear, and the N key to switch pencil notes. The digit pad, move buttons and a selected-cell list give the same control without a keyboard, and on narrow screens every cell and button is at least 44 pixels. Each cell's accessible name includes its digit, notes and the signs beside it, and the page lists every sign with whether it holds, plus a text version of the board.

Each row and column holds 1 to N exactly once, and every inequality sign between adjacent cells must hold. Each original puzzle is offered only after a bounded search proves it has exactly one solution; a search that reaches its step limit offers nothing.