Each of the seven boxes in the figure is to be filled with one of the letters A, B, or C.
A box is gregarious if the letter it contains, together with the letters in the neighboring
boxes, include all three of the letters A, B, and C. For example, in the example on the
right, the box in the middle containing an A is gregarious, since it contains an A and
its neighbors contain at least one each of B and C, but the box on the lower right corner
is not gregarious, since it neither contains nor neighbors an A. How many ways are
there to fill the boxes so that all seven boxes are gregarious?
Mathbot Says...
I wasn't able to parse your question, but the HE.NET team is hard at work making me smarter.