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A little logic. A satisfying break.

How to play Futoshiki

Put the numbers in order. Fill each row and column once, and let the inequalities guide you.

Play Futoshiki

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Numbers and inequalities

  1. Every row and column contains each number from 1 to the board size exactly once. A 4 × 4 board uses 1, 2, 3 and 4.
  2. Follow every inequality. The pointed end faces the smaller value; the open end faces the larger value.
  3. Starting clues and inequality signs are fixed. There are no boxes, regions or diagonal restrictions.

For a vertical sign, ∧ means the top cell is smaller than the bottom cell. ∨ means the top cell is larger. Each sign and its adjacent cells also announce the relation with row and column names.

Work from what you know

Before

After

Action: Enter 3 in column 3: it is the only missing number in this four-cell row.

One missing number

On a 4 × 4 board, the row 1 4 □ 2 needs 3 in the gap. It must also satisfy its column and every touching inequality.

Read a chain

On a 4 × 4 board, A < B < C means A cannot exceed 2 and C cannot be below 3: there must be room for three strictly increasing numbers. A bent or vertical chain works the same way. Follow each sign’s direction, not the shape of the line.

First scan almost-complete rows and columns, then use the small and large ends of inequalities. Combine checked deductions; a plausible guess is not a proof.

Checked techniques

Peer Single

A placed value excludes itself from the rest of its row and column.

Hidden Single

A missing number with only one possible location in a row or column belongs there.

Edge Range

An inequality excludes values outside its possible lower and upper range.

Placed Edge

A placed inequality endpoint bounds the value on the other side.

Edge Support

Keep an endpoint value only if a compatible value remains across its inequality.

Increasing inequality chain

Follow a directed path of strictly increasing inequalities. Each edge requires at least one step up in value. In A < B < C, C is at least two greater than A: the upper bound of C limits A, and the lower bound of A limits C. Keep the path in its inequality direction.

Naked Set

A set of cells reserving the same number of values excludes those values elsewhere in its unit.

Hidden Set

Values confined to the same number of cells exclude other values from those cells.

Controls, notes and recovery

Ctrl+Z or Command+Z undoes the last edit or whole applied hint. Ctrl+Shift+Z or Command+Shift+Z redoes; Ctrl+Y also redoes. These work from the active board and its action buttons. Text fields keep their native editing shortcuts. Settings saves this game’s optional timer and Auto-check choice independently. Turn Auto-check off and use Check when you want to review your work.

Tap or click a cell, then choose a number or Erase. Arrow keys move selection; 1 through the board size enters a number. Delete, Backspace or 0 erases. N toggles Notes. In Notes mode, choosing a number toggles that candidate in an empty cell.

Matching displayed numbers and pencil marks follow your selection. Hold a pad digit with a mouse or pen to inspect it without entering; touch-hold locks its highlight. Shift+number on a board cell locks or unlocks that digit. Unlock highlight is also available. With a digit locked, Space enters it or toggles its note. Inspection never checks the hidden answer or writes progress. Fixed clues and paused play stay protected.

Entering a number clears that cell’s notes and removes incompatible notes from its row, column and directly connected inequalities. Undo restores both entries and notes. Redo, restart, Check and the optional timer work as on your other boards.

Get a hint checks the current entries and independently checks the deduction sequence before suggesting a placement. Expand Checked deductions to follow its premises and eliminations. Notes are reminders, not proof: hints derive their possibilities from the rules, so an omitted note cannot justify a number. Apply makes one ordinary entry, including note cleanup. It works once; edits, navigation or a new hint invalidate an earlier suggestion. Undo restores the prior board.

Progress saves locally. Your space brings all seven games together, latest played first. Share a code or link for the original board. Download and restore progress to transfer entries, notes and timer. Restore asks before replacement; conflicting or unreadable saves keep their own recovery controls and do not erase other games.

Two levels on 4 × 4 and 5 × 5; Easy on 6 × 6

Start with 4 × 4 Easy. Easy uses row/column singles and basic inequality bounds. Medium adds candidate support and directed chains. These are computational technique levels, not human or publisher calibration. Hard and 6 × 6 Medium are not offered for New.

Relaxed play has no mistake limit. The optional three-mistake challenge lets you continue relaxed after three mistakes. The optional timer pauses when the board is hidden or paused. Futoshiki offers New, Next and saved/shared boards; Today’s Futoshiki and the published archive offer shared puzzles when available.