Question 50
A number of $N$ children are at a party, and they sit in a circle to play a game of Pass the Parcel. Because the host has no other form of entertainment, the parcel has infinitely many layers. On turn $i$, starting with $i = 1$, the following two things happen in order:
(1) The parcel is passed $i^2$ positions clockwise; and
(2) The child currently holding the parcel unwraps a layer and claims the prize inside. For what values of $N$ will every child receive a prize?
(1) The parcel is passed $i^2$ positions clockwise; and
(2) The child currently holding the parcel unwraps a layer and claims the prize inside. For what values of $N$ will every child receive a prize?