Decagon Adjacency Challenge
Combinatorics · proposed by @Jarz43021
A regular decagon has its sides labeled with the integers 1, 2, 3, ..., 10, with each label used exactly once.
The labels are arranged around the decagon. For every pair of adjacent sides, the sum of their labels must be a prime number.
Two arrangements are considered identical if one can be obtained from another by a rotation or reflection of the decagon.
How many distinct arrangements are possible?