Question 9
Donkeys numbered $1,\ldots,n$ around a circle say D,O,N,K,E,Y repeatedly, starting at 1. A donkey saying Y leaves; counting continues at the next donkey with D, until one remains. When $n=186$, the winner is 10. Find the smallest $n\gt186$ for which the winner is 100.
For four donkeys, the first one to say Y is number 2; after further counting, number 1 leaves, then number 4. Number 3 wins.
For four donkeys, the first one to say Y is number 2; after further counting, number 1 leaves, then number 4. Number 3 wins.