Card-passing puzzle

[Edwin Clark]

On Wed, 8 Oct 2003, Rob Arthan wrote:

> 
> Someone recently posted a challenge on sci.math that may be of interest to 
> sequence fans and may have some interesting sequences associated with it.
> 
> It is a game played by n players with n-1 cards. Each player is dealt a random 
> number of the cards. Play then proceeds in rounds: in each round, each player 
> with at least two cards passes one card left and one card right. I'm taking 
> this as meaning all players play in parallel in each round, not in turn.
> 
> The challenge is to prove that the game always terminates. I.e., eventually no 
> player will have more than one card. I have signally failed to do this so 
> far.
> 

For what it is worth, I have just verified that the game always terminates
for n <=9 players no matter how the n-1 cards are dealt. I did it using
brute force with Maple. 

--Edwin