MathDB

A number of

N

children are at a party and they sit in a circle to play a game of Pass and 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 chidren receive a prize?

Patrick \ Winter \, United \ Kingdom

Problem Statement