[Edu-sig] casino math (unit three)

[Laura Creighton]

In a message of Mon, 31 Aug 2009 22:23:55 PDT, kirby urner writes:

<snip>

>On break, we encourage playing with Pysol maybe...
>
>http://www.pysol.org/
>http://pysolfc.sourceforge.net/
>http://tktable.sourceforge.net/tile/
>http://pygames.sourceforge.net/
>
>Kirby
>4D

I think that the pysol game 'Pile On' is always solvable.
Anybody know for sure?  Writing a program that exhaustively creates
all the possible layouts and then solves them seems possible, but
I keep thinking there has to be a more elegant proof in there.

rules here for those unfamiliar with the game (googling for 'Pile
On' seems to generate a myriad of false positives).

Pile On
One-Deck game type. 1 deck. No redeal.

Begin:
The game begins with 13 piles of 4 cards, ina random order, plus 2 empty piles.

Goal:
Rearrange the cards so that each pile contains four cards with the same rank.

Rules:

Cards can be moved on top of any other card or cards of the same rank,
or to empty piles.  Groups of cards can be moved if they are of the
same rank.

A pile cannot have more than four cards, and an empty slot can be
filled with any card or group of cards with the same rank.

___________

So, simple.  But always solvable?  I am not sure about that.

Laura