Consider the twelve configurations c1

, c2

, ..., c12

in Figure 1.4. For every two configurations ci

and cj

, where 1 i, j 12, i j, it may be possible to obtain cj

from ci by first shifting one of

the coins in ci horizontally or vertically and then interchanging the two coins. Model this by a

graph F such that V(F) = {c1

, c2

, ..., c12} and cicj

is an edge of F if ci and cj can be transformed

into each other by this 2-step process.