MathDB

Suppose

n\geq 3

is an integer. There are

n

grids on a circle. We put a stone in each grid. Find all positive integer

n

, such that we can perform the following operation

n-2

times, and then there exists a grid with

n-1

stones in it:

\bullet

Pick a grid

A

with at least one stone in it. And pick a positive integer

k\leq n-1

. Take all stones in the

k

-th grid after

A

in anticlockwise direction. And put then in the

k

-th grid after

A

in clockwise direction.

Problem Statement