# Kowalewski's Settlement Problem for Triacontahedron

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Kowalewski's diagram consists of 30 non-overlapping simply connected regions. Each region has four neighboring regions. There are also 30 two-digit values. The Kowalewski settlement problem is to place values on regions so that each region's value has exactly one common digit with each neighboring value.

Contributed by: Izidor Hafner (July 2019)

Open content licensed under CC BY-NC-SA

## Details

Kowalewski's original condition is a little stronger. Two opposing neighboring signs 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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