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Futoshiki
Futoshiki, meaning "not equal" in Japanese, is a logic puzzle from Japan also known as "More or Less." It is played on a small square grid where you place numbers under both Latin-square rules and inequality constraints. The clues are the comparison signs printed between adjacent cells.
Futoshiki Rules
On an N×N grid you place the numbers 1 through N. Each number must appear exactly once in every row and exactly once in every column, like a Latin square. A few cells may start filled in as givens.
Inequality signs (< and >) sit between some neighboring cells. The greater-than or less-than relationship must hold true for every pair the sign connects — the open mouth always points to the larger number.
You combine the no-repeat rule with the inequalities to deduce each cell. A valid Futoshiki has one unique arrangement that satisfies every row, every column, and every inequality at once.
Futoshiki Strategy & Tips
Anchor the extremes at chained signs
A run of signs like a < b < c on a 5-grid forces values near the limits — the smallest cell in a long ascending chain often must be 1, the largest must be near N.
Use inequalities to split candidates
If a > b, then a cannot be the lowest value and b cannot be the highest. Pencil in candidates and trim each cell's range using the sign before applying row and column logic.
Cross-hatch like Sudoku
Because each number appears once per row and column, placing a value eliminates it from the rest of that line. Track where a given digit can still legally go.
Find forced values at the boundary
A cell pressed by a > toward a known small number, or a < toward a known large one, may have only one survivor. Combine the inequality squeeze with the digits already placed nearby.
Frequently Asked Questions
How do the greater-than signs work in Futoshiki?
Each < or > sign between two cells states which is larger. The wide, open end points at the bigger number, and that relationship must always be satisfied.
What does Futoshiki mean?
Futoshiki is Japanese for "not equal" or "inequality," reflecting the comparison signs that drive the puzzle.
Can a number repeat in a Futoshiki row?
No. Like a Latin square, each number from 1 to N must appear exactly once in every row and once in every column.
Is Futoshiki related to Sudoku?
They share the no-repeats-in-a-line rule, but Futoshiki has no boxes and adds inequality constraints, and its grids are usually smaller — commonly 4×4 to 7×7.