• Corpus ID: 3916812

The Convex Configurations of "Sei Shonagon Chie no Ita" and Other Dissection Puzzles

  title={The Convex Configurations of "Sei Shonagon Chie no Ita" and Other Dissection Puzzles},
  author={Eli Fox-Epstein and Ryuhei Uehara},
The tangram and Sei Shonagon Chie no Ita are popular dissection puzzles consisting of seven pieces. Each puzzle can be formed by identifying edges from sixteen identical right isosceles triangles. It is known that the tangram can form 13 convex polygons. We show that Sei Shonagon Chie no Ita can form 16 convex polygons, propose a new puzzle that can form 19, no 7 piece puzzle can form 20, and 11 pieces are necessary and sufficient to form all 20 polygons formable by 16 identical isosceles right… 

Symmetric Assembly Puzzles are Hard, Beyond a Few Pieces

On the negative side, it is shown that the problem is strongly NP-complete even if the pieces are all polyominos, and on the positive side, the problem can be solved in polynomial time if the number of pieces is a fixed constant.

Determining the essentially different partitions of all Japanese convex tangrams.

The set of the 16 possible convex tangrams that can be composed with the 7 so-called "Sei Shonagon Chie no Ita" (or Japanese) tans is considered and all essentially different solutions with the "Japanese" tans are presented.

Finding all convex tangrams

The final author version and the galley proof are versions of the publication after peer review and the final published version features the final layout of the paper including the volume, issue and page numbers.



A Theorem on the Tangram

2. Lemmas. It is easily seen that the tangram can be divided into sixteen equal isosceles right triangles. For the sake of convenience, we call the legs and the hypotenuses of these right triangles

http://www.matsusaki.jp/ local-event

  • http://www.matsusaki.jp/ local-event
  • 2014