Futoshiki
Puzzle · 11 playsFutoshiki
A Latin square governed by greater-than signs — every inequality must hold.
About Futoshiki
A Japanese logic puzzle whose name simply means inequality. Fill the grid so that every row and every column contains each number from 1 up to the grid size exactly once, while keeping every < or > sign printed between neighbouring cells true. Those few arrows carry a remarkable amount of information: a chain of rising signs can pin down an entire line before you have placed a single number by counting. Free to play in your browser — no download, no sign-up.
How to Play
Every row and column must contain each number from 1 to N exactly once. The < and > signs between two cells always point at the smaller of the pair. Tap a cell and pick a number. Chains of signs settle the highest and lowest values first.
Tips & Strategy
The signs are worth more than the given numbers. Chase the chains first: in a 5×5 grid, three cells linked a < b < c mean a can be at most 3 and c at least 3. A chain of four rising cells in a 5-grid pins the ends completely — the lowest must be 1 or 2, and the top of a four-chain cannot be less than 4.
The extremes are your entry point. The largest value N can never sit on the small side of a sign, so any cell with a > pointing away from it toward a neighbour is still eligible, but a cell pointing into a > from the small end can never be N. Likewise, 1 can only live in a cell with no < pointing out of it. Sweeping the grid for where N and 1 can legally go usually places two or three numbers straight away.
Once a few cells are down, treat it as a Latin square and use standard candidate work. Pencil in candidates, then look for naked pairs in a row or column — two cells sharing the same two candidates strip those digits from every other cell in that line. Hidden singles, where a value fits only one cell of a row, appear constantly here because the inequalities knock out so many options.
Re-check every sign after each placement, not just the row you were working on. A number placed in a column often tightens an inequality two cells away that you had already written off, and that cascade is where the puzzle unravels. If you are genuinely stuck, take the tightest sign chain on the board and test its lowest cell as 1 — the contradiction, when it comes, usually arrives within three or four forced moves.