# Wilson, exercise 10.4

We **fail** to prove this configuration colorable.

We color the boundary nodes with all 27 possible color combinations,
modulo equivalence of colors, that are consistent with this smaller
configuration:

We see no way to color the configuration given
any of the 8 following boundary rings (though other rings, listed below, work):

In case you were interested in the successful parts,

18 successes are simple and 1 requires Kempe-chains.

## Easily colorable boundary node color-arrangements

## Kempe chain possibilities for RB/GY on

with color-flipped boundary nodes marked with heavy dashes. (Apologies for the kempe chain edges passing through things visually.)