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bonanova's post in Clock (an old favorite of mine) was marked as the answer
The problem sounds familiar, but I don't think it has been posted.
Here is my approach.
A very fine puzzle indeed.
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bonanova's post in Rolling a coin was marked as the answer
No need to spoiler.
If it has made a complete revolution, (and it has) it's facing the same "way" after as before.
Maybe I'm missing something.
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bonanova's post in May 2013 POM - Puzzle-of-the-Month - Golf ball Dimples was marked as the answer
OK I have it.
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bonanova's post in A man travels between five cities was marked as the answer
The old traveling salesman problem.
Tractable for five cities, but unimaginably complex with just a few more cities.