How to play Futoshiki

Futoshiki is a Japanese number puzzle. The name means "not equal". You fill a square grid with numbers, guided by a few given numbers and by greater-than and less-than signs between neighbouring squares.

The rules

1. On an n×n grid, use the numbers 1 to n. A 5×5 grid uses 1 to 5.
2. Each row contains every number exactly once.
3. Each column contains every number exactly once.
4. Every sign must hold. The open side faces the bigger number: in 3 > 1 the left square is bigger. Signs between rows work the same way: ∨ means the top square is bigger, ∧ means the bottom square is bigger.

Every GridBites puzzle has exactly one solution, and you never need to guess.

Techniques that solve most grids

The ends of a chain

A square that is bigger than its neighbour can never be 1, and a square that is smaller can never be the top number. A chain of three signs pointing the same way, such as a < b < c < d on a 5×5 grid, leaves very little room: a can only be 1 or 2, and d only 4 or 5.

Where can the 1 go?

Pick a number and a row, and ask which squares could hold it. The 1 cannot sit on the bigger side of any sign; the top number cannot sit on the smaller side. Often only one square is left.

Squeezed between two signs

A square with a smaller neighbour on one side and a bigger neighbour on the other sits in the middle of a chain. In a 4×4 grid, a square that is bigger than one neighbour and smaller than another must be 2 or 3.

Finish rows and columns

When a row has only one or two empty squares left, the missing numbers usually fall straight out. Check the columns that cross them before you write anything in.

Controls

• Tap a square, then tap a number below the grid. Tap Erase to clear it.
• On a keyboard: type a number, Backspace to erase, arrow keys to move, Ctrl+Z to undo.
• Numbers that break a rule turn red straight away.
• Your progress and time are saved in this browser, so you can close the tab and come back.

Ready? Play today's Futoshiki or start with a quick 4×4 warm-up.