Futoshiki Solver Online

What is a Futoshiki solver?

A Futoshiki solver is an online tool that completes an inequality puzzle by applying the standard Futoshiki rules. Every row and column must contain the numbers from 1 to the grid size, with no repeats, and every greater-than or less-than sign must be true.

This page is built for people searching for Futoshiki solver, Futoshiki puzzle solver, inequality puzzle solver, greater than less than puzzle solver, Futoshiki answers, Futoshiki helper and online Futoshiki calculator.

• Solve a Futoshiki from a newspaper, app, book or printable worksheet.
• Check whether your current entries are still possible.
• Find the next logical Futoshiki move without revealing the whole answer.
• Test a handmade inequality puzzle for validity and uniqueness.

How to use this Futoshiki solver

Choose the grid size first. In number mode, click a square and enter any known value with the number buttons or keyboard. In sign mode, click a gap between two neighbouring squares to cycle through less-than, greater-than and blank.

Press Solve to complete the puzzle. Press Check to confirm that the numbers you have entered can still fit a valid solution. Press Next move if you want a hint that shows candidates, highlights the important cells and names the technique.

• Use 4x4 or 5x5 for quick Futoshiki puzzles.
• Use 6x6 to 9x9 for larger inequality puzzles.
• Click horizontal gaps for signs between left and right cells.
• Click vertical gaps for signs between upper and lower cells.
• Apply a logical move only when you want the tool to update the grid.

Futoshiki rules used by the solver

The solver assumes the normal Futoshiki rules. A 5x5 puzzle uses the numbers 1 to 5 in every row and column. A 7x7 puzzle uses 1 to 7. There are no Sudoku-style boxes.

The inequality signs, sometimes called chevrons, compare adjacent cells only. A sign between A and B says that one of those two values must be larger. Even though the sign is local, it can create long chains of forced candidates.

• Rows cannot repeat a number.
• Columns cannot repeat a number.
• A greater-than sign must point from the larger value to the smaller value.
• A less-than sign must place the smaller value before the larger value.
• Every filled number must stay within the grid range.

Next move logic and Futoshiki strategies

The Next move helper begins with pencil marks. It removes any number already used in the same row or column, then removes values that cannot satisfy a neighbouring chevron. For example, if A > B in a 5x5 grid, A cannot be 1 and B cannot be 5.

After the basic eliminations, the helper looks for naked singles, hidden singles, naked pairs, hidden pairs and X-wings. It also lets inequality chains keep trimming candidates as new values are placed or removed.

• Naked singles place a cell with one remaining candidate.
• Hidden singles find a value that has only one possible position in a row or column.
• Naked pairs reserve two values in two matching cells.
• Hidden pairs keep two values that appear only in the same two cells.
• X-wings remove a candidate locked into the same two positions across two rows or columns.

Why a Futoshiki puzzle may have no solution

A Futoshiki can become impossible if a row or column repeats a number, if an inequality sign contradicts two placed values, or if a chain of signs leaves a cell with no legal candidate.

A puzzle can also have multiple solutions. Published Futoshiki puzzles normally aim for one answer, but a handmade grid with too few numbers or signs may allow several finished boards. The solver checks for that and reports when the clues are not unique.