Question 158
There are $n$ children around the round-table. Erika is the oldest among them and she has $n$ candies. No other child has any candy. Erika decided to distribute the candies and determined following rules. In every round all the children with at least two candies show. Erika chooses one of them and he/she sends one by one candy to both children sitting next to him/her. (So in the first round only Erika shows and sends one by one candy to her two neighbours.) For which $n \geq 3$ is it possible to end the distribution after a finite number of rounds with every child having exactly one candy?