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
_______________________________________________
Edu-sig mailing list
Edu-sig@python.org
http://mail.python.org/mailman/listinfo/edu-sig
_______________________________________________
Edu-sig mailing list
Edu-sig@python.org
http://mail.python.org/mailman/listinfo/edu-sig
