How to play Futoshiki
Futoshiki is a compact logic puzzle built on a simple idea: fill a square grid so no number repeats in any row or column, while obeying the greater-than and less-than signs between cells. There are often very few starting numbers, so the signs carry most of the information. Grids here range from 4×4 to 8×8 and grow as your rating rises.
The rules
- On an N×N grid, fill every cell with a number from 1 to N. A 6×6 grid uses 1 to 6.
- Each row must contain every number exactly once.
- Each column must contain every number exactly once.
- Every sign between two neighbouring cells must be true. The open side of < or > always faces the bigger number; vertical signs work the same way, turned on their side.
Click a cell and type or tap a number; arrow keys move around and Backspace clears. A wrong number turns red and counts as an error. Each sign turns green once both its cells are filled and it holds, and red if it is broken.
Getting started
Begin with the extremes. On a 5×5 grid, any cell that is smaller than a neighbour cannot be 5, and any cell that is larger than a neighbour cannot be 1. Now suppose row 2 has a chain of signs running across columns 1 to 4, each cell smaller than the next. Four rising numbers drawn from 1 to 5 leave little room: row 2, column 1 must be 1 or 2, and row 2, column 4 must be 4 or 5. If column 1 already contains a 1 elsewhere, row 2, column 1 is the 2, and the cells to its right must be 3, 4 and 5 in order. That also places the 1 in row 2, column 5.
Switch on Notes, or press N, to keep pencil marks of the candidates in each cell. When you place a correct number, it is automatically removed from the notes in its row and column, which keeps your marks tidy as the grid fills up.
Strategies and tips
- Trim the ends. A cell with a sign saying it is smaller than a neighbour can never be the largest number; a larger cell can never be 1. Apply this to every sign before doing anything else.
- Follow chains. In a chain of k rising cells, the first cell is at most N − k + 1 and the last is at least k. Long chains, including ones that turn corners, pin numbers down quickly.
- Propagate bounds. If a cell can only be 2 or 3 and its neighbour must be smaller, that neighbour can only be 1 or 2. Keep pushing these limits along the signs until nothing changes.
- Hidden singles. Look at one number in one row. If every cell but one is excluded by the column or by a sign, that number goes in the remaining cell.
- Count what is missing. On larger grids, list the numbers still missing from a nearly complete row or column and check which empty cells can take each one.
How the difficulty adapts
The page has five levels, 400 rating points apart, and each one changes the grid size: Easy is 4×4 (rating 1000), Medium 5×5 (1400), Hard 6×6 (1800), Expert 7×7 (2200) and Master 8×8 (2600). Every new puzzle uses the level nearest your current rating. The generator first strips the grid down to the fewest numbers and signs that still give exactly one solution; on Easy and Medium it then adds a few clues back to make the start gentler.
Solving within the target time (3 minutes on Easy, rising to 20 on Master) with three errors or fewer earns +80 rating points. More errors, or going over time, costs 160, and each hint costs another 80. The rating never drops below 800. A run of clean solves therefore takes you to a bigger grid, while a few difficult games bring you back down.
The reason for all this: a puzzle that is always slightly hard keeps you thinking, while one you can finish on autopilot does little. Challenge that keeps pace with your skill is better training. For background, see what research says about puzzles and brain health.
A short history of Futoshiki
Futoshiki comes from Japan, and its name roughly means "inequality". Like sudoku, it is based on the Latin square, a grid in which every symbol appears once per row and column, an idea mathematicians have studied for centuries. The puzzle reached a wider audience in the mid-2000s, when British newspapers, riding the popularity of sudoku, started printing it alongside other Japanese logic puzzles. Its small grids and clean rules have made it a favourite for quick daily solving.
Frequently asked questions
Does each puzzle have only one solution?
Yes. Every clue is removed only if the puzzle still has exactly one solution, so logic alone always gets you there.
Why are there so few starting numbers?
On the harder levels the signs do most of the work. Sometimes a grid starts with almost no numbers, and the inequalities alone fix the answer.
How do hints work?
Select a cell that is empty or wrong and press Hint to reveal its correct number. Each hint costs 80 rating points, so use them when you are truly stuck.
Is my rating saved?
If you are signed in, your rating is stored in your account. Otherwise it resets when you reload, but you can jump to any grid size with the difficulty buttons.