MathDB

N

boxes are arranged in a circle and are numbered

1,2,3,.....N

In a clockwise direction. A ball is assigned a number from

{1,2,3,....N}

and is placed in one of the boxes.A round consist of the following; if the current number on the ball is

n

, the ball is moved

n

boxes in the clockwise direction and the number on the ball is changed to

n+1

n<N

and to

1

n=N

. Is it possible to choose

N

, the initial number on the ball, and the first position of the ball in such a way that the ball gets back to the same box with the same number on it for the first time after exactly

2020

rounds

Problem Statement