MathDB

In the game of "Fingers",

N

players stand in a circle and simultaneously thrust out their right hands, each with a certain number of fingers showing. The total number of fingers shown is counted out round the circle from the leader, and the player on whom the count stops is the winner. How large must

N

be for a suitably chosen group of

N/10

players to contain a winner with probability at least

0.9

? How does the probability that the leader wins behave as

N\to\infty

Problem Statement