Determining the essentially different partitions of all Japanese convex tangrams

In this report we consider 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, see [9]. The set of these Japanese tans is slightly different from the well-known set of 7 Chinese tans with which 13 (out of those 16) convex tangrams can be formed. In [4], [5] the problem of determining all essentially different partitions of the 13 “Chinese” convex tangrams was investigated and solved. In this report we will address the same problem for the “Japanese” convex tangrams. The approach to solve both problems is more or less analogous, but the “Japanese” problem is much harder than the “Chinese” one, since the number of “Japanese” solutions is much larger than the “Chinese” ones. In fact, only for a few “Japanese” tangram shapes their solutions can be found by a rigorous analysis supported by a large number of clarifying diagrams. The solutions for the remaining shapes have to be determined using a dedicated computer program. Both approaches will be discussed here and all essentially different solutions with the “Japanese” tans are presented. As far as we know all presented results are not yet published before.