APMO 1991 Problem-4
Posted: Thu Feb 02, 2012 9:43 am
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.
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.