What is Futoshiki?
Futoshiki is a number-placement logic puzzle played on a square grid. A 5x5 Futoshiki uses the numbers 1 to 5, a 6x6 puzzle uses 1 to 6, and so on.
The twist is the inequality signs between adjacent cells. If one cell points to another with a greater-than sign, the first value must be larger. These signs turn a simple Latin square into a sharper deduction puzzle.
- Each row contains every number from 1 to the grid size.
- Each column contains every number from 1 to the grid size.
- No number repeats in a row or column.
- Every greater-than and less-than sign must be true.
- Given numbers cannot be changed.
How to play Futoshiki
Start by scanning the signs. A cell that must be less than another cell cannot be the maximum number. A cell that must be greater than another cell cannot be the minimum number.
Then combine those limits with row and column rules. If a row already contains 1, 3 and 4 on a 4x4 grid, the last empty cell must be 2, provided the surrounding inequalities agree.
- Click or tap an empty cell.
- Use the number buttons or keyboard to enter a value.
- Use Check to highlight values that disagree with the solution.
- Use Hint to reveal one correct cell.
- Use New puzzle to generate another board at the same settings.
Grid sizes and difficulty
The 4x4 Futoshiki is fast and friendly for learning the signs. The 5x5 grid is the classic middle ground, while 6x6 creates longer chains of row, column and inequality logic.
Difficulty changes how much structure is visible at the start. Easy puzzles include more givens and signs. Hard puzzles leave more cells open, so you need to combine several small constraints before a number becomes forced.
- 4x4: quick beginner puzzles and short breaks.
- 5x5: balanced Futoshiki with enough room for chains.
- 6x6: larger grids with deeper elimination.
- Easy: more direct placements.
- Hard: fewer obvious starts and more linked deductions.
Futoshiki strategy tips
Look for extremes first. A cell that is greater than two neighbours is unlikely to be 1, and a cell that is less than two neighbours is unlikely to be the highest number. These limits are often enough to remove candidates.
Chains are especially powerful. If A is less than B and B is less than C, then A cannot be one of the largest values and C cannot be one of the smallest values. Combine that with row and column exclusions to find forced cells.
- Mark cells that cannot be the minimum or maximum.
- Use rows and columns to remove repeated numbers.
- Follow chains of inequalities before guessing.
- Recheck every sign after placing a number.
- Treat a solved row or column as new information for crossing cells.
A worked Futoshiki example
The fastest way to feel Futoshiki is to follow a chain of signs. Picture a row in a 5x5 puzzle with A < B < C < D < E running left to right. Each cell must be larger than the one before, the row uses 1 to 5 exactly once, and the only ordering that fits is 1, 2, 3, 4, 5 — the whole row is solved from a single chain.
Shorter chains still pin the ends. With just A < B < C, cell A can be at most 3 because it needs two larger values above it, and cell C is at least 3 because two smaller values sit below it. That instantly deletes 4 and 5 from A and 1 and 2 from C, and the leftover candidates usually fall to ordinary row and column scanning.
- Read each sign as 'this cell is smaller than that one'.
- A full increasing chain across a line fixes the whole line.
- The low end of a chain cannot hold the largest values.
- The high end of a chain cannot hold the smallest values.
- Finish the cell with normal row and column elimination.
Reading inequality bounds exactly
Every sign is really a counting limit. In an n x n grid the values are 1 to n, so a cell that must be larger than k other cells in its chain is at least k + 1, and a cell that must be smaller than k others is at most n − k. A cell with two smaller cells below it can therefore never be 1 or 2.
These bounds are the quickest way to place the extremes. The number 1 can only sit in a cell that is not forced to be larger than anything, and n can only sit in a cell that is not forced to be smaller than anything. Hunt for those cells first, then let each placement tighten the bounds on its neighbours.
- A cell with k smaller cells in its chain is at least k + 1.
- A cell with k larger cells in its chain is at most n − k.
- Only a cell with no greater-than requirement can be 1.
- Only a cell with no less-than requirement can be n.
- Each placement narrows the bounds on the cells it points to.
Futoshiki, Sudoku and the Latin square
Futoshiki shares its core with Sudoku: fill the grid so every row and column holds each number exactly once. The difference is that Futoshiki has no 3x3 boxes — that grid rule on its own is simply a Latin square, the centuries-old object studied by mathematicians like Euler. What makes the puzzle is the layer of inequality signs placed between cells.
So Futoshiki is a Latin square with constraints: the row-and-column rule narrows the candidates, and the < and > signs do the rest. The name is Japanese for 'not equal,' and you will also see the puzzle published as Unequal. Because it drops the boxes and adds order clues, it rewards a different instinct from Sudoku — thinking about which values are bigger, not just which are missing.
How this online Futoshiki generator works
This page creates a solved Latin-square grid, adds true inequality signs between neighbouring cells, and then removes visible clues while checking that the puzzle still has a single solution.
Each generated board stays on this main Futoshiki page, giving players a fresh puzzle while keeping the SEO focus on one evergreen guide to Futoshiki rules, strategy and online play.