Kowalewski's Settlement Problem for the Rhombic Dodecahedron
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.
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).