Futoshiki

What is Futoshiki?

Futoshiki is a Japanese number puzzle. You fill a square grid with numbers, and no number may repeat in a row or a column. Small signs between some squares tell you which number is bigger. This page lets you play Futoshiki online free, from easy 4×4 grids up to 7×7 expert puzzles, plus a new daily Futoshiki.

Futoshiki rules

• A grid of size N uses the numbers 1 to N. A 5×5 grid uses 1, 2, 3, 4 and 5.
• Every row has each number exactly once.
• Every column has each number exactly once.
• A sign between two squares must be true. < and > work left to right. ∧ means the top number is smaller. ∨ means the top number is bigger.
• Yellow numbers are given at the start. You cannot change them.
• Every puzzle here has exactly one solution. You never need to guess.

How to use the buttons

• Tap a square, then tap a number below the board. Tap the same number again to clear it.
• ✏️ Notes switches to pencil marks. Use it to write small candidate numbers in a square.
• ↶ Undo takes back your last move. ⌫ Erase clears the selected square.
• 💡 Hint fills one correct square. Your result shows how many hints you used.
• ⟲ Reset starts the puzzle again. ‹ › move between levels.
• On a keyboard: arrow keys move, 1–9 type, Backspace clears, N toggles notes, Ctrl+Z undoes.
• Red numbers or red signs show a clash. Your progress, times and daily streak are saved in this browser.

What Futoshiki does for your mind

Futoshiki is small, but it asks for real thinking. Here is what you practise while you play:

• Logic. Every step is a small “if this, then that”. If a square must be smaller than a 2, it can only be 1.
• Ordering and comparing. Chains of signs, like a < b < c, make you think about order. In a 4×4 grid, a chain of four squares can only be 1, 2, 3, 4.
• Working memory. You keep several possible numbers in mind at once. Notes help, but you still juggle them.
• Focus. One careless number breaks a row. The puzzle rewards slow, steady attention.
• Patience and planning. Bigger grids do not open at once. You learn to look for the one safe step, then the next.
• A calm break. A 4×4 or 5×5 takes only a few minutes. It is a quiet pause without news or noise.
• A sense of achievement. The last number clicks into place, and you know the answer is right.

What science says, honestly

There is no study on Futoshiki itself that we know of. There is research on brain exercises in general. In September 2026 the University of Southampton reported on its “Active Brains” trial, published in The Lancet Primary Care. More than 11,500 people aged 60 to 85 with cognitive impairment took part. After 12 months, the group that used a website with brain exercises and advice had 8% fewer people with mild cognitive impairment than the control group, according to the university's press release. That is a link between brain-stimulating activity and better results. It is not proof that one puzzle protects your brain. Enjoy Futoshiki because it is fun and makes you think.

Who is it for?

• Beginners and children: start with 4×4. It teaches the idea in a few minutes, and the numbers stay small.
• Sudoku fans: the row and column rule is the same, but the signs give you a new way to think.
• Daily players: the 📅 Daily puzzle changes every day and keeps a streak.
• Experts: 7×7 puzzles have few clues and need long chains of reasoning.
• Older players: big numbers, no time pressure and no ads inside the board. Play at your own pace.

Futoshiki tips and strategy

1. Look for the ends. A square that is bigger than something can never be 1. A square that is smaller than something can never be N.
2. Follow chains. In a chain a < b < c, the first square is at most N−2 and the last is at least 3.
3. Use the given numbers. If a square must be bigger than a 4 in a 5×5 grid, it must be 5.
4. Write notes early. On 6×6 and 7×7, mark candidates in the tight squares first.
5. Count what is missing. If a row needs only 2 and 5, check which square can take the 5.
6. Find the only place. Ask “where can the 1 go in this column?” Often only one square works.
7. Check both directions. A sign affects the number before and after it. Update both.
8. Don't guess. Each puzzle has one solution. If you are stuck, look again for a chain you missed.

A short history of Futoshiki

The name futōshiki (不等式) means “inequality” in Japanese. According to Wikipedia, the puzzle was developed by Tamaki Seto in 2001. It became popular in Britain after the Sudoku wave. In 2006 The Guardian ran a piece titled “If you were seduced by sudoku, prepare for futoshiki fever”. Today it appears in several UK newspapers, such as The Guardian and The Times.

Fun fact 1: a solved Futoshiki is a “Latin square” – a grid where each symbol appears once in every row and column. Mathematicians studied Latin squares long before this puzzle existed.

Fun fact 2: Simon Tatham's free puzzle collection calls the game “Unequal”. It also has an “Adjacent” mode, where bars mark numbers that are next to each other, like 3 and 4.

Questions people ask

More logic games

• 📅 Daily Sudoku
• 🧮 Kakuro
• 👑 Crown Grid
• 🔳 Nonogram
• 🧩 Sudoku

Guides: Sudoku tips for beginners · Brain training: the truth · Puzzle trends this week

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Sources

• Wikipedia – Futoshiki
• Simon Tatham's Portable Puzzle Collection – Unequal
• University of Southampton – Active Brains trial (Sept 2026)

This page is for fun and general information, not medical advice.