MathDB

In a pond there are

n \geq 3

stones arranged in a circle. A princess wants to label the stones with the numbers

1, 2, \dots, n

in some order and then place some toads on the stones. Once all the toads are located, they start jumping clockwise, according to the following rule: when a toad reaches the stone labeled with the number

k

, it waits for

k

minutes and then jumps to the adjacent stone.
What is the greatest number of toads for which the princess can label the stones and place the toads in such a way that at no time are two toads occupying a stone at the same time?
Note: A stone is considered occupied by two toads at the same time only if there are two toads that are on the stone for at least one minute.

Problem Statement