# futoshiki.app — full summary

Canonical URL: https://futoshiki.app
Publisher: futoshiki.app (contact: malam169@gmail.com)
Category: Free online puzzle game (logic / number puzzle), single player, browser-based, no account.

## What it is

Futoshiki is a logic puzzle played on a square grid of N×N cells. The player places the digits 1 to N so that no digit repeats within any row or column and every inequality sign between two neighbouring cells is satisfied. Some cells are pre-filled ("givens"). The name is Japanese for "inequality" (不等式). futoshiki.app offers a free, client-side implementation with boards from 4×4 to 9×9 in Easy and Hard.

## Rules

1. Each row contains each digit from 1 to N exactly once.
2. Each column contains each digit from 1 to N exactly once. There are no boxes or regions (unlike Sudoku).
3. A sign between two adjacent cells points at the smaller number. In a row, "<" means the left cell is smaller and ">" means the left cell is larger. Between vertically adjacent cells, "∧" means the upper cell is smaller and "∨" means the upper cell is larger.
4. Given digits cannot be changed.
5. Signs compare only the two cells they sit between.
6. Every puzzle has exactly one solution and is solvable by logic alone.

## How puzzles are made

Puzzles are generated in the browser. A random Latin square is built by permuting rows, columns and symbols of a cyclic square. The generator then starts with every given and every inequality sign and removes clues in random order, keeping a removal only if a backtracking solver (most-constrained-cell ordering, with bound propagation across signs) still finds exactly one solution. Easy stops when about nine clues remain per ten cells; Hard continues until no further clue can be removed with provable uniqueness. If the solver's search budget is exhausted the clue is kept, so uniqueness is never assumed.

## Controls

- Mouse / touch: select a cell, then a digit on the number pad. Tapping the same digit again clears the cell. Digits already placed N times are disabled.
- Keyboard: arrow keys move the selection; 1–9 enter a digit; Backspace, Delete or 0 clear the cell; P toggles pencil notes; H gives a hint; U or Ctrl+Z undoes; N starts a new puzzle; M mutes or unmutes sound.
- Pencil notes: in notes mode the digits toggle small candidates in the selected cell. Placing a real digit removes that digit from the notes of every cell in its row and column.
- Undo: unlimited, covers digits, notes, erases and hints.
- Hint: fills one wrong or empty cell (the selected one if possible) with its correct digit. Hints are counted; a solve with hints does not set a best time.
- Live checking: duplicate digits and unsatisfied signs are shown in red. The board validates rules, not the stored answer.

## Sizes and difficulty

- Sizes: 4×4, 5×5, 6×6, 7×7, 8×8, 9×9.
- Difficulty: Easy or Hard. Stats and best times are kept separately for each of the twelve combinations.

## Solving strategy summary

- Start with the extremes: N cannot be on the small side of a sign; 1 cannot be on the big side.
- Follow chains such as a < b < c: a is at most N−2 and c is at least 3. A chain spanning a whole row forces 1..N in order.
- Use givens next to signs to bound their neighbours.
- Look for hidden singles: a digit that fits in only one cell of a row or column.
- Use pairs: two cells in a line sharing the same two candidates exclude those digits from the rest of the line.
- Use pencil notes on boards of 6×6 and above.

## Sound, storage and privacy

- Sound effects are synthesized with the Web Audio API (no audio files). Mute with M or the speaker button; the setting persists.
- Local storage keys are versioned and namespaced: futoshiki:progress:v1 (settings and stats) and futoshiki:game:v1 (the unfinished puzzle, restored on refresh).
- No accounts, no server-side game state. Google Analytics (GA4) records aggregate traffic and events such as starting or solving a puzzle.

## Accessibility

Full keyboard play; every cell announces its row, column, value, given status and attached signs; controls have explicit labels; WCAG AA contrast in light and dark themes; respects reduced-motion preferences.

## Origin

The puzzle is generally credited to Tamaki Seto, published in Japan in 2001, and later spread through newspapers and puzzle sites, where it is also known as "Unequal".

## Pages

- https://futoshiki.app/ — play
- https://futoshiki.app/how-to-play — rules and controls
- https://futoshiki.app/tips — strategy
- https://futoshiki.app/faq — frequently asked questions
- https://futoshiki.app/about — about and origins
- https://futoshiki.app/privacy — privacy policy
- https://futoshiki.app/terms — terms of use