In a message of Wed, 02 Sep 2009 03:29:36 +0200, Gregor Lingl writes: >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 pil >es >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. I don't think that it is quite as bad as all that, given that all we really have is a set of 52 cards which are 4 sets of 13 cards with different marks on them. Thus there is a significant reduction you can make at the start because an initial set where all the 8s are swapped for all the 4s are equivalent. But then, I wasn't really looking for the brute-force proof, but the elegant one. I was hoping for an induction proof for 4 sets of 4 cards, n cards, and n + 1 cards, but so far I haven't managed it. >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 :-( Don't believe the strategy that pysol gives about not stacking 3 cards of a same rank on a single. As far as I can tell that is nonsense. But do keep track of what cards are on the bottom. >Thanks for the deverting hint >Gregor You are most welcome. :-) Laura _______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
