There is no finite master list of all tangram puzzle solutions: the classic set has seven fixed pieces, but those pieces can form an open-ended range of silhouettes, and some targets have more than one valid arrangement. This guide explains the standard rules, gives you a practical way to approach a target, and points to activities that include actual puzzles and solutions.
What counts as a tangram puzzle solution?
A standard tangram has seven pieces, traditionally called tans: two large right triangles, one medium right triangle, two small right triangles, one square, and one parallelogram. A classic silhouette puzzle asks you to use all seven pieces to fill or form a target shape. Keep the pieces flat, do not overlap them, and follow the puzzle’s rules about whether pieces must touch and whether the target must be filled completely.
As Michelle Manes puts it in the tangrams section of Mathematics for Elementary Teachers: “Whenever you solve a tangram puzzle, your job is to use all seven pieces to form the shape.” Read the tangrams section.
Targets can depict animals, people, objects, or geometric figures. A silhouette usually shows only the outer boundary, so solving it means working out which pieces fit inside that outline—not matching a single prescribed arrangement. More than one arrangement may work. The University of Cambridge’s NRICH square activity includes multiple student solutions and notes that there are more possibilities when the square does not have to be completely filled.
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How to solve a tangram puzzle
There is no guaranteed quick procedure for every silhouette. Treat the following as a practical sequence for testing placements, not as a universal algorithm.
- Check the rules and inventory. Confirm that the puzzle uses all seven pieces, whether the outline must be filled, and whether pieces may be flipped. Count the two large triangles, medium triangle, two small triangles, square, and parallelogram before you begin.
- Study the outline. Look for long straight edges, sharp corners, and broad regions. These give you clues about which pieces might fit, but a visual resemblance alone does not prove a placement.
- Try the large triangles in broad areas. Rotate them to test whether their long sides and points align with substantial parts of the target. Avoid locking in a placement if it leaves an awkward region that the remaining pieces cannot fill.
- Test the square and parallelogram. Rotate them to find regions with compatible edges. Flip a piece only if the puzzle allows it; the parallelogram’s orientation can matter.
- Use the smaller triangles to refine the fit. Try them around corners and narrower sections, then reconsider earlier placements if gaps remain.
- Check the completed boundary and piece count. A candidate solution should use every piece exactly once, keep pieces inside the target, and have no overlaps or unintended gaps. Also check that the pieces touch if the activity requires a connected shape.
Where to find tangram puzzles with solutions
These activities provide ways to manipulate pieces or try specific challenges. Their formats differ, so check each activity’s directions before assuming it uses the same fill and contact rules as another.
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| Resource | How you work with it | Challenges and solutions | Teaching or rules notes |
|---|---|---|---|
| NRICH, University of Cambridge: “Tangrams” | Interactive activity. | Includes a square challenge and student solutions; the activity discusses multiple possible arrangements. | Includes teacher guidance. Its square task distinguishes between filling the square completely and allowing other solutions. |
| Science Museum of Minnesota / Science Learning Network: “Tans” | Provides a pattern for making pieces and challenge figures. | Challenge designs have linked solutions. | Offers activity guidance; follow the page’s instructions for its particular challenges. |
| Michelle Manes, “65 Tangrams,” in Mathematics for Elementary Teachers | Suggests making pieces from a printable pattern. | Provides shape problems to try. | Explains the seven-piece challenge and offers teaching-oriented context. |
If you would rather work away from a screen, use a standard seven-piece set or print a pattern and cut out the tans. Hands-on pieces make rotation and rearrangement easy to test; an interactive activity is convenient when you want to try a challenge directly in a browser.
Does “all solutions” mean every possible tangram arrangement?
No practical page can list every target silhouette and every valid arrangement. The answer depends on which outline you are solving, the rules for filling it, and whether different placements count as distinct solutions. For a particular target, use an activity that labels the silhouette and its corresponding solution rather than assuming that one diagram is the only possible answer.
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- TANGRAM PUZZLE PACK 30 KIDS PARTY FAVORS - Set of 30 tangram puzzle in individual bags, perfect for gifting to boys and girls as goodie bags stuffers for kids. With its 7 pieces, kids can create the 94 figures from the attached guide or simply let their imagination soar. Each tangram puzzles measure 3.9 x 3.9 inches, making them ideal as birthday party favors for kids
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There is a narrower mathematical count: ETH Library, ETH Zurich, reports that 13 convex polygons can be constructed from the seven tans. That figure applies only to convex polygons—not to all silhouettes, all target shapes, or all valid arrangements. The library attributes the result to a 1942 article by two mathematicians at the National University of Chekiang, without naming them on its page. See ETH Library’s tangram account.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.When did the tangram originate?
Published accounts differ, so a precise origin date should not be treated as settled. The University of Hawaiʻi textbook gives a date of about 1100 during China’s Song Dynasty, while ETH Library says the puzzle in its present form was first documented in China in the early nineteenth century. These are different historical claims; neither should be silently substituted for the other.
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