Futoshiki
A Latin square puzzle with inequality constraints.
The rules
How to play
- 01
Fill the Latin square
Futoshiki (Japanese for “not equal”) is played on an N×N grid. Fill every cell with a single digit from 1 to N.
- 02
Unique rows
Each row must contain every digit from 1 to N exactly once — the same digit can never repeat within a row.
- 03
Unique columns
Each column must also contain every digit exactly once, so no value is duplicated down any column.
- 04
Read the signs
A greater-than or less-than sign between two adjacent cells shows which neighbour holds the larger value: A < B means A is smaller than B.
- 05
Satisfy every inequality
A finished grid obeys all the inequality signs at once, alongside the row and column rules — every constraint holds simultaneously.
Play smarter
Six ways to read the signs
Chase the extremes
In a run like A < B < C < D < E on a 5×5, A is forced to 1 and E to 5. Chains of signs pin their endpoints.
Eliminate as you place
The moment a digit lands, strike it from every other cell in that row and column to narrow the field.
Squeeze the signs
A sign next to a known digit narrows its neighbour instantly: a cell reading 3 > ___ can only hold 1 or 2.
Find forced positions
When constraints leave a digit only one legal cell in a row or column, place it there without hesitation.
Cross the two rules
A candidate that survives both the Latin-square rule and the surrounding inequalities is often the only choice.
Pencil the candidates
Note the possible digits for tight cells so the right value reveals itself as rows, columns and signs resolve.
Watch & learn
Two minutes to mastery
From the Intel desk
Reading for the curious
Futoshiki Puzzle: A Complete Beginner's Guide to Inequality Logic
Learn how to solve Futoshiki puzzles from scratch. Master the rules, understand inequality constraints, follow our visual step-by-step tutorial, and discover essential strategies for this elegant number-placement puzzle.
Logic Puzzles for Kids: How Puzzles Build Math-Ready Minds (Ages 6-8)
Research-backed guide for parents on how logic puzzles develop working memory, spatial reasoning, and problem-solving skills in children ages 6-8. Includes age-appropriate puzzle recommendations and practical tips.
Futoshiki Strategies: Mastering Inequality Chains
Master Futoshiki with inequality chain analysis, boundary elimination, and cascade techniques. Solve complex grids with pure logic, no guessing.
Keep going
Where to next
Fresh every day
The Daily Futoshiki
One shared grid for everyone, every day. Build a streak and compare your solving time.
Go deeper
Rules & strategy guide
From extreme values to forced positions — the complete written guide with worked examples.
Beyond the grid
Explore all puzzles
Sudoku, Nonograms, Slitherlink and fifteen more logic games await.