[Edu-sig] casino math (unit three)

[Gregor Lingl]

Laura Creighton schrieb:
> 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, 
Hi Laura,
I fear that this is not  practicable.  There are 52! =
80658175170943878571660636856403766975289505440883277824000000000000
permutations of 52 cards. If one considers the permutations of the 13 piles
as equivalent and also the permutations of the four suits one still 
arrives at a number
of possible Pile On games that exceeds by far the number of nanoseconds 
that passed
since the beginning of the universe.
> but
> I keep thinking there has to be a more elegant proof in there.
>   
Yes, I would also be interested in such a proof. I for my part learned 
to know Pile On
only today and I find it rather difficult to play. So from my own very 
irrelevant
experience would expect that there are start configurations which might 
not be solvable -
--- at least for me :-(

Thanks for the deverting hint
Gregor

P.S.: According to your suggestion I wrote an ugly little program, that 
up to now
was able to solve all the sample start configurations I fed it with. ;-)

> 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
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