# Card-passing puzzle - clarification

Rob Arthan rda at lemma-one.com
Wed Oct 8 17:51:32 CEST 2003

```On Wednesday 08 Oct 2003 4:23 pm, Meeussen Wouter (bkarnd) wrote:
> if n is even ...
>
>    0   0   4   0
>    0   1   2   1
>    0   2   0   2
>    2   0   2   0
>    0   2   0   2
> ...
> ad nauseam?

No - that's 4 players and 4 cards,  but the rules (see snippet below) are n
players and n-1 cards.

You are correctly pointing out that the claim is the strongest possible one:
if there are n cards then there is always a way of dealing them which would
stop the game terminating - as you've done if for even n and like this for
odd n:

2 0 2 0 1
0 2 0 1 2

ad nauseam, because the second arrangement is a cyclic permutation of the
first.

Regards,

Rob.

> -----Original Message-----
> From: Rob Arthan [mailto:rda at lemma-one.com]
> Sent: woensdag 8 oktober 2003 17:10
> To: seqfan at ext.jussieu.fr
> Subject: Re: Card-passing puzzle - clarification
>
> On Wednesday 08 Oct 2003 3:45 pm, Rob Arthan wrote:
> > 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.
> >...
>
> Whoops! I should have added that they're sitting round in a circle so
> everybody has exactly one player to their left and one to their right.

```

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