Find the number of ways of arranging the numbers 1, 2, 3, ... 9 in a circle, so that the sum of any three adjacent numbers is divisible by 3. (Two arrangements are considered the same if one arrangement can be rotated to obtain the other.
Just put them in a circle in order 1 -2 -3-4-5-6-7-8-9 voila! (well....that is ONE way)
and here is another 1-3-5-7-9-2-4-6-8