MathDB

In the lake, there are

23

stones arranged along a circle. There are

22

frogs numbered

1, 2, \cdots, 22

(each number appears once). Initially, each frog randomly sits on a stone (several frogs might sit on the same stone). Every minute, all frogs jump at the same time as follows: the frog number

i

jumps

i

stones forward in the clockwise direction. (In particular, the frog number

22

jumps

1

stone in the counter-clockwise direction.) Prove that at some point, at least

6

stones will be empty.

Problem Statement