Futoshiki

How to play Futoshiki

Futoshiki is a number puzzle from Japan. The name means "not equal". The board is a square grid, 5×5, 6×6 or 7×7. Between some squares you see small signs: < and > between squares side by side, and ∧ and ∨ between squares above each other. A few squares may already hold a number.

Goal

Fill every square with a number from 1 up to the size of the grid (1 to 5 on a 5×5 grid). Each number must appear exactly once in every row and every column. Every sign must be true: the sign always points at the smaller number, and its open side faces the bigger one. Each puzzle here has exactly one answer, and you can always find it with logic.

Step by step

1. Pick a square with a tap or a click, or move with the arrow keys. Its row and column light up.
2. Enter a number with the pad under the grid or with the number keys.
3. Turn on Notes (or press N) to write small pencil marks for numbers that might fit. Placing a number clears the same note from its row and column.
4. Use Erase or Backspace to clear a square, and Undo (Ctrl+Z) to take back a step.
5. If a number repeats in a line, both squares turn red. If two numbers break a sign, the sign turns red too.

Reading the signs

A chain of signs tells you a lot. In a 5×5 grid, a square that is smaller than another square can never be 5. A square at the end of a chain of four "less than" signs must be 5, and the one at the start must be 1.

Levels

Easy is a 5×5 grid with many signs and a few numbers to start. Medium is 6×6 with fewer signs. Hard is 7×7 with only the signs you really need.

End of the game

You win when every square is filled correctly. The timer stops and shows your time. Your game is saved in this browser, so you can come back later. Like it? Try Sudoku or Calcudoku next.

Strategy tips

• Start with the ends of chains. A square that is bigger than another can never be 1, and a square that is smaller can never be the top number. Long chains pin down the 1s and the top numbers fast.
• Count the chain. If a square sits above three smaller squares in a chain, it must be at least 4. Write this limit in your notes.
• Look for the only place. In each row, ask where the 1 can go. Often only one square is not blocked by a sign or a number in its column.
• Use notes on Hard. Write the possible numbers in each square, then cross them off as you learn more. A square with one note left is solved.
• Squares between two signs are squeezed. A square that is bigger than one neighbour and smaller than another can never be the lowest or the highest number.