Futoshiki
Futoshiki is a logic puzzle on a square grid with greater-than and less-than signs between some neighbouring cells. Fill each row and column with the digits from 1 up to the grid's size, once each, so that every sign points at the smaller of its two digits.
How to play
Every Futoshiki here has exactly one solution and can be solved by logic alone. The grid grows from 5×5 at Easy to 7×7 at Expert, and the level is set by the hardest technique the puzzle needs.
- Each row and each column holds every digit from 1 to the grid size once.
- A sign between two cells points at the smaller digit.
- The given digits cannot be changed.
Playing on this site
- Select a cell, then type a digit or tap it on the number pad. Arrow keys move the selection.
- Turn on Notes (or press N) to pencil in candidates instead of answers.
- A sign turns red when the digits on its two sides break it.
- Hint first points out any wrong digits, then names the next technique and shows where it applies before giving anything away.
- Your puzzle is saved in this browser, so you can come back to it later.
Techniques by level
Every technique the solver knows, from easiest to hardest. A puzzle's level is the hardest one it needs.
Easy
- Hidden single
- In the highlighted row or column this digit fits in only one cell.
- Greater and smaller
- The smaller side of a sign must stay below the largest digit the other side can take, and the larger side above the smallest.
Medium
- Naked pair
- Two cells share the same two candidates, so those digits leave the rest of their area.
- Hidden pair
- Two digits fit only in the same two cells, so those cells hold nothing else.
Hard
- Naked triple
- Three cells hold only three digits between them, so those digits leave the rest of their area.
- Hidden triple
- Three digits fit only in the same three cells, so those cells hold nothing else.
- X-Wing
- A digit is limited to the same two columns in two rows (or the reverse), so it leaves the rest of those lines.
Expert
- Contradiction
- Try another digit in the marked cell and a rule breaks a few steps later. So that digit is out.
Questions
How do the signs help?
A cell on the larger side of a sign can never hold 1, and one on the smaller side never the largest digit. Chains of signs push these limits further, so a run of three increasing cells must start at 3 or less.
Will I ever have to guess?
No. Every puzzle has exactly one solution that logic alone reaches, at every level.
Is Futoshiki free to play here?
Yes. Every level is free, with no account and no sign-in.