How is Futoshiki different from Sudoku?

Both are Latin-square puzzles — no repeats in rows or columns. Sudoku also forbids repeats within 3×3 boxes, while Futoshiki uses inequality signs ( ) between adjacent cells instead. Futoshiki grids are usually smaller (4×4 to 9×9), and the inequality constraints create a different style of deduction.

Play Futoshiki Online

Q: What is Futoshiki?

Futoshiki (Japanese for 'not equal') is a logic puzzle played on an N×N grid. You must fill every cell with a number from 1 to N so that no number repeats in any row or column. Some adjacent cells are connected by greater-than (>) or less-than (<) signs that must also be satisfied. It combines the Latin-square logic of Sudoku with inequality constraints.

Fill every row and column with the numbers 1 to N — no repeats allowed. Obey the > and < inequality signs between cells. Pure logic, zero guesswork.

Time

0:00

Filled

0/16

Wins

Select a cell and enter a number

What Is Futoshiki?

Futoshiki (不等式, Japanese for "inequality") is a logic puzzle that combines the Latin-square constraint of Sudoku with greater-than and less-than signs between adjacent cells. The result is a deeply satisfying deduction puzzle that rewards careful chain-of-logic reasoning.

The rules are simple: fill an N×N grid with the numbers 1 to N so that no number repeats in any row or column, and every inequality sign between two neighbouring cells is satisfied. A > sign means the left (or top) cell must contain a larger number than the right (or bottom) cell, and < means the opposite.

How to Play

Choose your grid size and difficulty. 4×4 Easy is great for beginners. Larger grids and harder difficulties give fewer starting numbers and signs.
Tap a cell to select it, then tap a number on the pad below to fill it in.
Use Notes mode (✏️) to pencil in candidate numbers when you're not sure yet.
Read the inequality signs carefully. A > between two cells means the left/top cell must be larger.
Check your work with the ✅ button. Errors are highlighted in red.
Complete the grid with no errors to win!

Futoshiki Strategy Tips

1. Follow the Chains

Look for chains of inequalities — for example, three consecutive > signs in a 4×4 grid force the sequence 4 > 3 > 2 > 1. Even shorter chains are extremely useful: two signs in a row limit the middle cell to specific values. Always scan the board for chains first.

2. Identify Extremes

If a cell has a > sign on both sides of it (pointing away), that cell must be large. In a 4×4 grid, it must be at least 3. Conversely, a cell with two < signs must be small. These extremes are the easiest cells to solve.

3. Use Row & Column Uniqueness

Just like Sudoku, if a number is already placed in a row, it can't appear again in that row. Cross-reference the inequality constraints with the uniqueness rule to eliminate candidates from unsolved cells. This is where pencil marks (notes mode) become essential.

4. Process of Elimination

If a cell can only hold one possible number after considering all constraints (inequalities, row uniqueness, column uniqueness), fill it in immediately. Each placement may trigger a cascade of further deductions — keep scanning the board after every move.

5. Think About Ranges

A > sign means the larger side must be at least 2 (it can't be 1), and the smaller side must be at most N−1 (it can't be N). Extend this logic along chains: the second cell in a chain of two > signs must be at least 3, and so on.

Futoshiki vs Sudoku

Both are Latin-square logic puzzles, but they differ in constraint type and feel:

Constraints: Sudoku uses 3×3 box uniqueness. Futoshiki uses inequality signs between adjacent cells.
Grid size: Sudoku is always 9×9. Futoshiki typically ranges from 4×4 to 9×9.
Deduction style: Sudoku is about elimination within boxes, rows, and columns. Futoshiki adds ordering logic — you reason about which cell is bigger or smaller.
Given numbers: Sudoku gives you about 25–35 starting digits. Futoshiki may give just a few numbers but provides inequality signs as additional constraint information.

History of Futoshiki

Futoshiki was popularised in the West through The Guardian newspaper, which began publishing the puzzle in 2006. The puzzle format originates from Japan, where inequality-based Latin-square puzzles appeared in puzzle magazines during the early 2000s.

The underlying concept — a Latin square with ordering constraints — has roots in combinatorial mathematics stretching back to Leonhard Euler's work on Latin squares in the 18th century. Modern Futoshiki combines this mathematical foundation with the puzzle-design principles refined by Japanese nikoli-style puzzle creators.

Today, Futoshiki appears in newspapers, puzzle books, and online platforms worldwide. Its unique blend of Sudoku-like row-column logic with inequality chain reasoning gives it a distinctive feel that has earned a dedicated following among puzzle enthusiasts.

Frequently Asked Questions

Futoshiki (Japanese for "inequality") is a logic puzzle played on an N×N grid. You must fill every cell with a number from 1 to N so that no number repeats in any row or column. Some adjacent cells are connected by greater-than (>) or less-than (<) signs that must also be satisfied. It combines the Latin-square logic of Sudoku with inequality constraints.

Both are Latin-square puzzles — no repeats in rows or columns. Sudoku also forbids repeats within 3×3 boxes, while Futoshiki uses inequality signs (< and >) between adjacent cells instead. Futoshiki grids are usually smaller (4×4 to 9×9), and the inequality constraints create a different style of deduction.

Start by looking for chains of inequalities. A chain of three > signs in a 4×4 grid forces the values 4 > 3 > 2 > 1. Next, use row and column uniqueness to eliminate candidates. Pencil marks (notes) help track possibilities. Finally, look for cells where only one number is possible after all constraints are applied.

Yes. A well-constructed Futoshiki puzzle has exactly one solution and can always be solved through pure logical deduction — no trial and error needed. The puzzles on this site are all generated to be solvable with logic alone.

This version offers 4×4, 5×5, 6×6, and 7×7 grids. Smaller grids are great for beginners, while 6×6 and 7×7 provide a serious challenge. Each size also has Easy, Medium, and Hard difficulty levels.

More Puzzle & Strategy Games

If you enjoy Futoshiki, try these other free games on our site:

Kakuro

Mathematical crossword — fill runs of cells so they sum to the clue with no repeated digits.

Nonograms

Fill a grid using row-and-column number clues — also known as Picross or Griddlers.