During a break, $n$ children at school sit in a circle around their teacher to play a game. The teacher walks clockwise close to the children and hands out candies to some of them according to the following rule:
He selects one child and gives him a candy, then he skips the next child and gives a candy to the next one, then he skips $2$ and gives a candy to the next one, then he skips $3$, and so on.
Determine the values of $n$ for which eventually, perhaps after many rounds, all children will have at least one candy each.
APMO 1991 Problem-4
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You spin my head right round right round,
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
- FahimFerdous
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Re: APMO 1991 Problem-4
I think I have a solution. It's quite logical. And I'm not sure how to arrange it actually. Rather I'd discuss it with Sourav and confirm. But my idea was to eliminate particular values of n and finally getting an answer.
Your hot head might dominate your good heart!