Is it possible to place the numbers 0,1,2,3,4,5,6,7,8,9 (not necessarily in this order) in a circle such that the difference between any two neighboring numbers is 3, 4 or 5?
If it is possible, show how; if it is impossible, prove that to be the case.
(In reply to re: hint (spoiler)
Thank you, Charlie, for your methodology and analysis of the problem.
I confirm having hyperlinked the foregoing in the official solution.