How to play
Futoshiki means “not equal” in Japanese, and the name says most of it. You fill a square grid with numbers, and the only clues besides a few given digits are the little inequality signs sitting between neighbouring cells.
Two rules, both strict:
- Each row and each column uses every number once. On a 4×4 grid that’s 1 to 4, on a 5×5 it’s 1 to 5, and on a 6×6 it’s 1 to 6.
- Every sign must be true. Between cells side by side you’ll see < or >. Between cells stacked in a column you’ll see ∧ (the upper cell is smaller) or ∨ (the upper cell is larger). Read them like in maths: the narrow point always faces the smaller number.
Tap an empty cell to select it, then tap a number on the panel below the grid. On a keyboard, type the digit, move with the arrow keys, and clear a cell with Backspace or Delete. Erase empties the selected cell, Undo takes back your last move and New puzzle deals a fresh grid.
Mistakes are flagged as you go. A number that repeats in its row or column is marked as an error, and so is any pair of your numbers that makes a sign false. Given digits are fixed and can’t be changed.
The three sizes
The Difficulty setting picks the grid size, and each size is built a little differently:
| Level | Grid | What you start with |
|---|---|---|
| Easy | 4×4 | Many signs and at least 4 given numbers |
| Medium | 5×5 | Fewer signs and at least 3 given numbers |
| Hard | 6×6 | Givens removed wherever the puzzle stays unique, then spare signs removed too |
Hard puzzles are pared down until any further removal would allow a second answer. Some open with very few numbers, and some with none at all, so the signs have to carry the whole solve. Every puzzle at every level has exactly one solution.
Strategy
Futoshiki rewards counting more than guessing. A few ideas take you a long way.
Chains fix their ends. In a row reading a < b < c, the first cell can’t hold the two biggest numbers and the last can’t hold the two smallest. A full chain of four across a 4×4 row is simply 1, 2, 3, 4.
Count the cells a number must beat. If a cell has to be larger than two different cells in the same row, those two are themselves different, so the cell is at least 3. If the two smaller cells sit in different lines (one in its row, one in its column), they might be equal, and you only learn that the cell is at least 2. This distinction catches people out.
The extremes are the easiest to place. The largest number can never sit on the narrow side of a sign, and 1 can never sit on the wide side. In each row, cross out every cell where the top number is impossible; often just one spot is left.
Use both lines at once. After placing a number, check its column as well as its row. Latin-square logic does most of the work, the same way it does in Sudoku, and a single placement often forces two more.
Hint is there when you’re stuck. It fills in one correct cell. If you’ve already written a wrong number somewhere, Hint fixes that cell first, which is a quiet way to learn where you went off track. Your hint count shows on the result screen when you finish.
If you like the Latin-square part but want arithmetic instead of signs, Math Cages uses the same grid sizes with arithmetic cages. Sudoku adds 3×3 boxes and drops the signs entirely.
If you enjoy Futoshiki, try Gumball Pop or Hidato next.
