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Heterocut

Subdivide the plane into a number of regions. All regions have a different shape, that is, no two pieces can be the same after rotation and/or mirroring. All region sizes are in the range given next to the puzzle. Arrows always point from a smaller to a larger region.

Example

The example puzzle deals with regions of size 2 to 5. To make this explanation easier, let's assign the digits 1 to 4 to the rows from bottom to top, and the letters A to D to the columns from left to right.

Let's start with the region in the upper left corner. It must have size of at least 3 due to the arrow pointing at it. Thus, we can determine that at least A4, A3 and B3 are all in the same region. Since A3 must be in a smaller region than the A2 region, this region must either be size 3 or 4.

The region containing B4, therefore, must be of either size 2 or 3. B4 and C4 must be in the same region, as must D4. Thus, this region has size 3, the region containing A4 must be of size 4, and the region containing A2 must be size 5. In order to have a size of 5, the remaining squares in that region must be A1-D1.

The remaining two uncompleted regions must now have a size of 4. If the upper left region takes C3 as its last square, then we will have two L shapes, which violates the rule that no two regions can be the same. Thus, the two remaining regions will consist of A4-A3-B3-B2, and the square of C3-D3-C2-D2.

Background

This genre was invented by Anurag Sahay from India and first appeared on the World Puzzle Championship in 2008.


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