# Kowalewski's Settlement Problem for the Rhombic Dodecahedron

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Kowalewski's diagram consists of 12 non-overlapping simply connected regions. Each region has four neighboring regions. There are also 12 two-digit labels. The Kowalewski settlement problem is to place the labels on the regions so that the labels of neighboring regions have exactly one common digit.

Contributed by: Izidor Hafner (August 2019)

Open content licensed under CC BY-NC-SA

## Details

Kowalewski's original condition is a little stronger. Two opposing neighboring labels must match the first digit and the other two the second digit. But if a solution with a weak condition is obtained, a solution with a stronger condition can be obtained by swapping some labels by exchanging the digits (e.g. 42 and 24).

Reference

[1] G. Kowalewski and D. Booth, "Construction Games with Kepler's Solid," Austin, TX: Parker Courtney Press, 2001. (Jul 16, 2019) www.zometool.com/content/KowalewskiWeb.pdf.

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