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.

1. Choose a grid size, such as 4x4, 5x5, 6x6, 7x7, or 8x8.
2. Fill each row with the digits 1 through N without repeats.
3. Fill each column with the digits 1 through N without repeats.
4. Obey every greater-than and less-than sign between neighboring cells.
5. Use candidates to track possible digits.
6. Finish when every cell has one number and all inequalities are true.

• 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.

• 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.

• 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.

• 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.
• 7x7 and 8x8 grids create massive inequality networks that test even expert solvers.

Play Futoshiki online for free. Fill the grid, obey every inequality, and use candidate ranges to solve without guessing.

Futoshiki is a clean inequality puzzle for Sudoku fans. Use signs, candidate ranges, and row-column uniqueness to place every digit.

• Futoshiki Rules Overview
• How Futoshiki Puzzles Work