What Is Futoshiki?
Futoshiki means 'inequality' in Japanese, and that one idea defines the puzzle. You fill an NxN grid with digits 1 through N so each row and column contains every digit once. Between some cells, greater-than and less-than signs tell you which neighbor must be larger. This creates a Latin-square puzzle with chains of order logic. A 5x5 grid can become surprisingly tense when one inequality chain controls three cells. Start with the signs, then narrow candidates.
How to Play Futoshiki
- Choose a grid size, such as 4x4, 5x5, or 6x6.
- Fill each row with the digits 1 through N without repeats.
- Fill each column with the digits 1 through N without repeats.
- Obey every greater-than and less-than sign between neighboring cells.
- Use candidates to track possible digits.
- Finish when every cell has one number and all inequalities are true.
Basic Rules
- A 5x5 puzzle uses digits 1 through 5.
- Rows cannot repeat digits.
- Columns cannot repeat digits.
- A greater-than sign points from the larger number toward the smaller comparison.
- Given numbers cannot be changed.
- A good puzzle has one solution.
Strategy Tips for Beginners
- Use inequality chains. In a 5x5 row, A > B > C means A cannot be 1 or 2, and C cannot be 4 or 5.
- Place extremes first. A cell greater than two neighbors is unlikely to hold a low digit.
- Combine row uniqueness with signs. If a row already has 5, any cell that must be greater than another cannot use 5.
- Watch reciprocal pressure. A cell smaller than one neighbor and larger than another has a narrowed middle range.
- Do not guess. Candidate lists and inequality ranges usually reveal the next move.
Real Examples of Gameplay
Simple Inequality
In a 4x4 grid, a cell marked greater than its neighbor cannot be 1, and the smaller neighbor cannot be 4.
Three-Cell Chain
A > B > C on a 5x5 grid means the only possible ordered triples must descend, such as 5-3-1 or 4-2-1.
Row Elimination
If a row already contains 2, and a cell must be less than 2, that cell must be 1.
Variations of Futoshiki
- Sudoku: Uses row, column, and box uniqueness without inequality signs.
- Calcudoku: Adds arithmetic cages to Latin-square placement.
- Killer Sudoku: Combines Sudoku regions with cage sums.
Why People Love Futoshiki
- Inequality signs create immediate deductions.
- Small grids solve quickly but still feel smart.
- The puzzle teaches ordered reasoning.
- It works well for players who like Sudoku but want fewer regions.
Play Futoshiki Online for Free
Play Futoshiki online for free. Fill the grid, obey every inequality, and use candidate ranges to solve without guessing.
Comparison
| Version | Difficulty | Players | Typical Time |
|---|---|---|---|
| 4x4 Futoshiki | Easy | 1 | 5 to 8 min |
| 5x5 Futoshiki | Medium | 1 | 8 to 15 min |
| 6x6 Futoshiki | Hard | 1 | 12 to 25 min |
Frequently Asked Questions
Is Futoshiki a math puzzle?
It uses number order, but no arithmetic. The digits act as ordered symbols.
What does a greater-than sign mean?
The number on the open side of the sign must be larger than the number on the pointed side.
Can a row repeat a number?
No. Each row and column must use each digit once.
Start Playing Now
Futoshiki is a clean inequality puzzle for Sudoku fans. Use signs, candidate ranges, and row-column uniqueness to place every digit.