From: Shlomi Fish <shlomif@shlomifish.org>
Date: Thu, 25 Oct 2012 09:50:04 +0200
Subject: Proposed Prune for Black Hole Solitaire and All in a Row Solitaire

Hi all,

you can read about Black Hole Solitaire here:
http://en.wikipedia.org/wiki/Black_Hole_%28solitaire%29 and about All in a Row
Solitaire here: http://www.goodsol.com/pgshelp/all_in_a_row.htm . I have written
solvers for them:

* https://bitbucket.org/shlomif/black-hole-solitaire

Now, what this games do is shed all cards from the columns into an
effectively single-active-card foundation by putting cards that are one higher
or one lower in rank (where King and Ace wrap). So I've been thinking that if
the solver reaches a situation where there are two or more separate
sub-sequences of ranks separated by ranks of which there are no cards, then
I can prune this state as unsolvable. E.g:

Rank 3 - 0 cards left
Rank 4 - 2 cards left
Rank 5 - 3 cards left
Rank 6 - 0 cards left
Rank 7 - 2 cards left

There is no way I will be able to put both the rank 7 cards and the rank 5 cards
there.

Another situation I've thought about is something like:

3: 0
4: 2
5: 1

Where 4->5 and 5->4 will yield the same problem, but generalising this will
require more complex analysis, and also some analysis of a
http://en.wikipedia.org/wiki/Hamiltonian_path , which is an NP-complete problem.

Regards,

	Shlomi Fish

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Shlomi Fish       http://www.shlomifish.org/
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