Tangram
Officially Tangram (Chinese Seven-Piece Puzzle / 七巧板 qīqiǎobǎn)
Ancient Chinese dissection puzzle — 7 flat geometric pieces (tans: 5 triangles, 1 square, 1 parallelogram) arranged to form thousands of shapes. Origin ~1815 Qing Dynasty; global craze 1810s-1820s (Napoleon owned one in exile); classic educational puzzle teaching geometry.
What is Tangram?
Tangram is a Chinese dissection puzzle consisting of 7 flat geometric shapes ('tans') that combine to form a square + can rearrange into countless silhouette shapes. Pieces: 5 TRIANGLES (2 large, 1 medium, 2 small), 1 SQUARE, 1 PARALLELOGRAM. All 7 fit together to form the source square. Rules: use ALL 7 PIECES, no overlap, form target silhouette. ~6600+ published tangram silhouettes across books/collections. ORIGIN ~1815 Qing Dynasty China (specific inventor unknown; earliest documented text 1813). Name '七巧板' (qīqiǎobǎn) = 'seven boards of skill.' EXPORTED to WEST via British trading ships 1815-1816; caused GLOBAL 'TANGRAM CRAZE' 1817-1825. NAPOLEON BONAPARTE played tangram during exile on Saint Helena (owned bone/ivory tangram set). LEWIS CARROLL owned tangram book. Popular Victorian parlor game. Modern uses: geometry teaching (elementary schools), spatial reasoning, art (tangram animals, letters, buildings). MATHEMATICAL: 13 CONVEX shapes possible with all 7 pieces (proven by Fu Traing Wang + Chuan-Chih Hsiung 1942). Related: STOMACHION (ancient Greek 14-piece puzzle attributed to Archimedes ~200 BC).
Quick facts
Category
Puzzle Games
Type
Individual
Players
1–4
Duration
~10 min
Where played
indoor
Field / court
flat surface
Country of origin
🇨🇳 China
Estimated origin
China ~1813-1815; global craze 1817-1825; Napoleon-era popularity; still-published tangram books today
Olympic
No
Popularity
global
How it works
Objective
Arrange 7 tans to match target silhouette using all pieces without overlap.
Match structure
Solo puzzle-solving or timed competitive. Some tangram tournaments exist informally.
Rules
Basic rules
7 pieces: use all
5 triangles + 1 square + 1 parallelogram; must use ALL 7 for valid solution.
No overlap
Pieces cannot overlap each other.
Match silhouette
Target shows outline only; arrange pieces to match.
Pieces can flip + rotate
Especially parallelogram (mirror image); all pieces freely oriented.
Advanced rules
13 convex shapes maximum
Only 13 convex silhouettes possible with 7 pieces (proven mathematically 1942).
Paradox puzzles
Two silhouettes look similar but one has missing part — famous 'monk' + 'headless monk' paradox showing perceptual illusion.
Categories: animals, people, objects, letters, numbers
6600+ published tangram silhouettes span many categories.
Speed tangram
Compete to solve identical silhouette fastest.
Digital solvers exist
Computer algorithms can solve any given silhouette; humans still enjoy the challenge.
Historical Chinese tangram books
Original Chinese collections had ~300-500 shapes; Western editions expanded to 1000-6600.
Scoring
Casual: solve = success. Competitive: fastest time wins.
| Action | Points |
|---|---|
| Solve silhouette | Success |
| Competitive time | Fastest = winner |
Win condition · Arrange all 7 pieces to match target silhouette.
Playing area
Called
flat surface
Dimensions
small — 7 pieces fit in 10-15 cm square
Any flat surface; pieces are 2D.
Equipment
Tangram set (7 pieces)
Wood, plastic, magnetic, or paper. $5-30. Solid colors typical (all one color or 7 different colors).
Tangram silhouette book
Collections of 500-2000 target shapes. $10-20.
Digital tangram apps
Free/paid mobile apps with hint systems + shape libraries.
Officiating
Casual game; no governing body.
- No formal officiating
Strategies
Start with easy silhouettes
Cats, birds, houses; build spatial intuition.
Place large triangles first
2 large triangles occupy 50% of area; anchoring them constrains rest.
Try flipping parallelogram
Parallelogram has mirror asymmetry; try both orientations.
Look for corner pieces
Right angles usually go in corners of silhouette.
Work paradox puzzles for perceptual insight
Sam Loyd's paradoxes teach how missing/added areas hide in geometry.
Use in classrooms
Elementary students learn geometry, fractions, symmetry through tangram.
Terminology
- Tan / Tans
- The 7 tangram pieces.
- Qiqiaoban (七巧板)
- Chinese name meaning 'seven boards of skill.'
- Silhouette
- Target outline for pieces to fill.
- Paradox puzzle
- Two silhouettes look similar but one has missing part (perceptual illusion).
- Convex shape
- Shape with no indentations; only 13 possible with all 7 pieces.
- Parallelogram tan
- The only piece with mirror asymmetry; can flip.
- Large/medium/small triangle
- Piece size categories.
- Stomachion
- Ancient Greek 14-piece dissection puzzle attributed to Archimedes.
- Napoleon tangram
- Famous historical anecdote — Napoleon owned bone/ivory set.
Major competitions
Informal school + educational events
occasional · worldwide (education) · since 1900
Where it is played
Governing bodies
No formal federation
N/A
Famous names & records
Famous athletes
- Napoleon Bonaparte (France, 1769-1821) — Owned bone/ivory tangram set during Saint Helena exile
- Lewis Carroll (UK, 1832-1898) — Alice's Adventures in Wonderland author; owned tangram books
- Fu Traing Wang + Chuan-Chih Hsiung — Mathematicians who proved 13 convex shapes possible (1942)
- Sam Loyd (USA, 1841-1911) — Puzzle master; published '8th Book of Tan' (1903) with fictionalized history
Records
Tangram origin
China Qing Dynasty — ~1813-1815 (1815)
Global tangram craze
Western world — 1817-1825 explosive spread (1820)
Napoleon's tangram set
Napoleon Bonaparte — Owned bone/ivory tangram during Saint Helena exile 1815-1821 (1820)
13 convex shapes proof
Wang + Hsiung — 1942 mathematical proof (1942)
Total published silhouettes
Collective tangram books — 6600+ across history (2020)
Learn this sport
beginner
- 1
Buy plastic/wooden tangram set ($5-10)
Physical tactile experience better than digital initially.
- 2
Solve 10-20 easy silhouettes
Cats, birds, houses; build spatial intuition.
- 3
Try tangram book with 500+ shapes
Comprehensive puzzle library for months of solving.
intermediate
- 1
Attempt paradox puzzles
Sam Loyd's classical paradoxes; understand perceptual illusion mechanics.
- 2
Compete against timer
Solo speed challenges; try to complete 20 silhouettes in 30 min.
- 3
Explore Stomachion + pentominoes
Related dissection puzzles; more pieces + complexity.
advanced
- 1
Study 13 convex shapes proof
Mathematical exploration of tangram limits.
- 2
Design own silhouettes
Create original tangram animals/objects.
- 3
Teach children
Elementary geometry classroom teaching; excellent educational tool.
Frequently asked
What is a tangram?+
Ancient Chinese dissection puzzle — 7 flat geometric pieces (5 triangles, 1 square, 1 parallelogram) that combine to form a square + can rearrange into thousands of silhouette shapes. Origin ~1815 Qing Dynasty China; caused global craze 1817-1825 in the West (Napoleon owned one). Rules: use ALL 7 pieces, no overlap, match target silhouette. 6600+ published silhouettes exist. Popular educational tool for teaching geometry, fractions, spatial reasoning.
How many tangram shapes are possible?+
TOTAL SILHOUETTES: unlimited (6600+ published across history). CONVEX SHAPES: exactly 13 possible (mathematically proven 1942 by Fu Traing Wang + Chuan-Chih Hsiung). Convex = no indentations. Non-convex silhouettes include people, animals, letters, buildings, geometric abstractions. Chinese original collections had ~300-500 shapes; Western books expanded to thousands. Modern digital apps have curated 1000+ challenges.
Did Napoleon really play tangram?+
YES — well-documented. Napoleon Bonaparte owned a BONE/IVORY tangram set during his EXILE ON SAINT HELENA (1815-1821). Historical records show he played extensively; the set survives + is displayed in museums. Coincidentally, tangram global craze occurred during his exile years (1817-1825), so Napoleon may have been among first Western enthusiasts. Also owned: LEWIS CARROLL (Alice author), Edgar Allan Poe (rumored), various Victorian intellectuals. Considered aristocratic parlor game 1820s Europe.
What is Sam Loyd's tangram paradox?+
Two-silhouette illusion PARADOX PUZZLE created by American puzzle master Sam Loyd (1841-1911) in '8th Book of Tan' (1903). Shows two 'monk' silhouettes — one COMPLETE, one 'HEADLESS' — both apparently using same 7 tangram pieces. Question: 'Where did the head go?' ANSWER: subtle area difference disguised by 90° rotation + repositioning; pieces don't actually create identical silhouettes despite appearance. Teaches PERCEPTUAL LIMITATIONS + geometric care. Loyd also wrote FICTIONALIZED HISTORY claiming tangram was 4000 years old — actually invented ~1815; falsified history persisted for decades.
Sources & provenance
- Wikipedia — Tangram— Wikipedia