[Edu-sig] casino math (unit three)
gregor.lingl at aon.at
Wed Sep 2 03:29:36 CEST 2009
Laura Creighton schrieb:
> In a message of Mon, 31 Aug 2009 22:23:55 PDT, kirby urner writes:
>> On break, we encourage playing with Pysol maybe...
> 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,
I fear that this is not practicable. There are 52! =
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
since the beginning of the universe.
> 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
experience would expect that there are start configurations which might
not be solvable -
--- at least for me :-(
Thanks for the deverting hint
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.
> The game begins with 13 piles of 4 cards, ina random order, plus 2 empty piles.
> Rearrange the cards so that each pile contains four cards with the same rank.
> 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.
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