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.
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
- Wikipedia — Futoshiki— Wikipedia