Question 6
The children in a class stand in a circle to play a candy game. The teacher gives each child an even number of candies (every child has candies, but their numbers may differ). A child gives half of their candies to the child immediately on their right. The child who has just received candies does the same if their new number is even; if it is odd, they receive one candy from the teacher before sharing in the same way. The children continue passing candies around the circle in turn. Prove that eventually there is a situation in which, if a child gives half of their candies to the teacher instead of to their neighbor, all children have equal numbers of candies.