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. combinatorics unsolvedcombinatorics