Question 4
During a break, $n$ schoolchildren sit in a circle around their teacher to play a game. Walking clockwise, the teacher chooses one child and gives that child a candy, skips the next child and gives a candy to the next, then skips $2$ children and gives a candy to the next, then skips $3$, and so on. Determine the values of $n$ for which eventually, perhaps after many rounds, every child receives at least one candy.