[Edu-sig] casino math, ooops sent this only to Gregor not the list

[Laura Creighton]

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.

>Very thrilling!

Glad to know the problem is keeping somebody else up thinking about
it too! :)

Best,
Laura

>
>Regards,
>Gregor

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