🔼 Futoshiki
🧩 Logic · 1 playsFutoshiki
A Latin square governed by greater-than and less-than signs.
About Futoshiki
Each row and column of the grid holds every number from 1 up to the grid's size exactly once — Sudoku without the boxes. In place of boxes there are inequality signs printed between some pairs of neighbouring cells, and each one must hold true in the finished grid. Chains of signs repay attention first: three cells reading less-than, less-than must start at 1 in a four-grid, and at 1 or 2 in a five. Nothing here needs to be guessed, and the puzzles are built so that it never pays to.
How to Play
Tap a cell and enter a number. Every row and every column must contain each number exactly once. Each < or > sign between two cells must be satisfied. Work the longest chains of signs first.
💡 Tips & Strategy
Start at the extremes, because the inequality signs bind them hardest. In a grid of size N, the value N can never sit at the small end of a sign, and 1 can never sit at the large end. Sweeping the board for those two exclusions alone usually removes a third of your candidates.
Chains multiply that effect. Where three cells run a greater than b greater than c, the first cell must be at least 3 and the last at most N minus 2, because two distinct values have to fit below and above them. The longer the chain, the tighter the squeeze on both ends.
Between chains, fall back on plain Latin square logic: each value appears exactly once per row and column, so a placement eliminates that value from two whole lines. Alternate between inequality reasoning and elimination rather than exhausting one before starting the other — each unlocks fresh moves for the other.
When a cell is down to two candidates, test them against every sign it touches. One of them almost always breaks a neighbouring constraint one or two steps along, which decides the cell without any guesswork.