Question 54
Suppose we assign one of positive integers $n$ satisfying $1 \le n \le 8$ to each of the 8 vertices of a regular octagon. How many ways of assigning these numbers are there, which satisfy the following 2 conditions?:
* assigned numbers are all distinct.
* any pair of numbers assigned to adjacent vertices are relatively prime.
Regard two assignments of 8 numbers to be distinct if one is obtained from the other by rotation or flipping of the octagon.
* assigned numbers are all distinct.
* any pair of numbers assigned to adjacent vertices are relatively prime.
Regard two assignments of 8 numbers to be distinct if one is obtained from the other by rotation or flipping of the octagon.