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Not quite right. There are some values of N>4 for which you won't want to take 3.
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Can't get stuck taking 3 on 11 or other prime numbers thereafter.
Edit: I'm at work so I can't fully flesh this out completely, but it would seem that 11, 13 and 17 screw you by taking three
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Actually maybe just 11 and 13. I don't know why but those numbers seem to screw you either way.
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You're right about 11. But with 13 you can avoid ending up with the last dumpling.
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Always 3, maximum allowed