[Edu-sig] casino math, ooops sent this only to Gregor not the list
lac at openend.se
Sun Sep 13 15:45:46 CEST 2009
In a message of Sun, 13 Sep 2009 15:21:12 +0200, Gregor Lingl writes:
>Laura Creighton schrieb:
>This pattern does not occur in my sample configuration:
> ( (11, 6, 2, 1),
> (11, 10, 4, 1),
> ( 9, 2, 6, 3),
> ( 9, 4, 8, 3),
> ( 7, 12, 10, 5),
> ( 7, 12, 2, 5),
> ( 5, 8, 4, 7),
> ( 5, 6, 12, 7),
> ( 3, 10, 8, 9),
> ( 3, 2, 6, 9),
> ( 1, 4, 10, 11),
> ( 1, 8, 12, 11),
> (13, 13, 13, 13),
> () )
>it has only even ranks in the second and third column, occurring
>pairwise in these columns, and odd ranks in the fourth one.
I don't think that it is a matter of being dealt them, sorry to
be unclear. I think you may have to make them and then break
them. So now it is not clear to me if your algorithm handles that.
>I do not have a special algorithm to solve Pile On, but only search
>the game tree using backtracking. Normally that gets out of hand.
>The point is that I believe to have found one *special* layout that
>can be investigated completely by hand, because due to its
>symmetries there occurs only a very limited set of possible moves.
Indeed, and thank you very much for it! :-)
>I think, that still some labour is needed to retrace my arguments.
>But if you are convinced (or only strongly believe) that I am wrong,
>you have an easier way to proof it: simply solve the configuration
>given above (and possibly show me, that resolving those patterns
>you displayed above is needed to do so.)
Yes indeed, and while I am quite busy this week, I will try to do
so. Right now I am trying to hack PySOL-FC so that you can
input a starting configuration of cards, and also save each state
change so that you can replay a game that you have won. But
today is not a day for hacking for me, so this will take me a
while to do.
Glad to know the problem is keeping somebody else up thinking about
it too! :)
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