Futoshiki

Officially Futoshiki (不等式)

JAPANESE LOGIC PUZZLE from the 2000s — solve a 5×5 (or 7×7) LATIN-SQUARE grid where each digit 1-N appears once per row + column, AND additional INEQUALITY (< or >) symbols between cells must all be satisfied. Name means 'INEQUALITY' in Japanese. Popular in newspaper puzzle sections + specialized puzzle books; contested in WORLD PUZZLE CHAMPIONSHIP grid-puzzle rounds since ~2005.

~10 min🌤indoor

Quick facts

Category

Puzzle Games

Type

Individual

Players

1–1

Duration

~10 min

Where played

indoor

Country of origin

🇯🇵 Japan

Estimated origin

Futoshiki puzzles appeared in Japanese puzzle magazines early 2000s; popularised in UK newspapers (The Guardian) mid-2000s; adopted by World Puzzle Championship (WPC) as regular puzzle type.

Olympic

No

Popularity

regional

How it works

Objective

Fill grid with digits so each ROW + COLUMN contains 1-N exactly once + all INEQUALITIES between adjacent cells hold.

Rules

Basic rules

  • Digits 1 to N used exactly once per row + once per column (Latin square)

    Signature Latin-square constraint.

  • INEQUALITY SIGNS (< or >) between adjacent horizontal or vertical cells must be respected

    Signature inequality constraint.

  • SOME DIGITS pre-filled as GIVENS to ensure unique solution

    Signature given-digits hint.

  • Puzzles have UNIQUE SOLUTION — logic only (no guessing needed for well-set puzzles)

    Signature unique-solution rule.

  • COMMON TECHNIQUES: FORCED DIGITS at extremes of inequality chains; scan for cells that must be MAX or MIN in row/column; scan pairs/triples

    Signature solve techniques.

Scoring

Correctness only; timed in competition (fastest correct solve = winner).

Win condition · Correctly filled grid; in WPC events, fastest correct time.

Equipment

  • PUZZLE GRID: standard 5×5 to 7×7; larger for competition

    Signature 5x5 grid.

  • PENCIL + ERASER (traditional) or DIGITAL app

    Standard writing tools.

  • INEQUALITY SYMBOLS (< > printed between adjacent cells at start)

    Signature inequality constraints.

  • SOME PRE-FILLED DIGITS as hints (givens)

    Signature givens/starting hints.

Terminology

Futoshiki
'Inequality' in Japanese.
Given
Pre-filled digit hint at puzzle start.
Inequality chain
Sequence of < signs establishing digit order (e.g., a < b < c).
Latin square
Grid where each digit appears once per row + column.

Major competitions

  • World Puzzle Championship (WPC — includes Futoshiki + Latin-square rounds)

    annual · Global (rotating host) · since 1992

  • UK Puzzle Championship

    annual · United Kingdom · since 2000

Where it is played

Governing bodies

  • World Puzzle Federation (WPF)

    Founded 1999 · Germany + Global

Famous names & records

Famous athletes

  • Ulrich Voigt (DE, multi-WPC champion)
  • Thomas Snyder (US, multi-WPC winner)
  • Palmer Mebane (US)
  • Jakub Ondroušek (CZ)

Sources & provenance

Last verified 2026-08-28.verified