Quote:
Originally Posted by d_m
then instead we need 260 tiles to cover all possible kinds of connectedness (1 + 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1).

Nitpick: that sums to 256, not 260. You can get that figure, as well as the 16 above, in a simpler way: each edge or vertex can be either connected or not connected, so 2 possibility for each of the 8 edges/vertices, 2^8=256.