Let's establish some ground rules. First of all, we are talking
about solvers here, not humans who can do just anything! I
was assuming some form of canonical move. For example,
I would only count 4 moves from the columns to home. Also,
I would only count one empty column as a target, the others
are redundant. Shlomi is right that moving an entire column
to an empty column is useless (redundant), but he forgot to
count the four moves from a column to a free cell. Again,
there are only 4 that are not redundant. Finally, I only count
the maximum move from a column to an empty column, not
all the shorter possibilities. These, are also redundant moves,
but the proof of that is beyond the scope of this email. Now,
applying these restrictions -- not counting any redundant
moves -- what do you calculate?
----- Original Message -----
From: "Shlomi Fish" <shlomif_at_iglu.org.il>
To: <fc-solve-discuss_at_yahoogroups.com>
Sent: Monday, May 04, 2009 12:58 PM
Subject: Re: A Puzzler for You
> Hi Gary!
>
> On Monday 04 May 2009 20:00:07 Gary Campbell wrote:
>> Sorry to reply to my own posting, but the
>> puzzle just got harder. I've now found a
>> way to demonstrate that the maximum
>> move fan-out is at least 41 moves! Can
>> anyone beat that?
>>
>
> Well, if we take the following layout (columns are lines):
>
> Freecells: - - - -
> Foundations: H-0 C-0 D-0 S-0
> : KH QC JH TC (all the way down to) AH
> : KC QH JC ... AC
> : KD QS JD ........................ AD
> : KS QD JS ........................ AS
> :
> :
> :
> :
>
> Then we can:
>
> 1. Move each of the sequences, or any parts there of to a different column.
> This makes a total of 4*13 == 52 moves, or even 4*4*13 == 208 moves if we
> consider every empty destination column as distinct.
>
> And we can also consider moving a sequence starting from a King card to a
> different column as a useless move.
>
> 2. We can move each one of the Aces to the freecell for a total of 4 or 4*4 ==
> 16 moves.
>
> So we get 52 different moves at the most pessimistic count, and 224 at the
> most "optimistic" one.
>
> Of course, not all of these moves are acceptable by Microsoft Freecell and its
> ilk, but I don't follow its guidelines strictly.
>
> Regards,
>
> Shlomi Fish
>
>> ----- Original Message -----
>> From: "Gary Campbell" <gary_at_numin8r.us>
>> To: <fc-solve-discuss_at_yahoogroups.com>
>> Sent: Monday, May 04, 2009 10:13 AM
>> Subject: A Puzzler for You
>>
>> > Has anyone ever determined the maximum
>> > number of possible moves there could be
>> > from a given free cell card layout?
>> >
>> > Can anyone think of a way to get more
>> > than 32? I think I can see how to get 32,
>> > but I'm not positive. And I don't off hand
>> > see how to get more.
>> >
>> > You'd think that anyone who's been
>> > working on a solver for almost 7 years
>> > would have asked and answered this
>> > question long ago!
>> >
>> > -Gary Campbell
>
> --
> -----------------------------------------------------------------
> Shlomi Fish http://www.shlomifish.org/
> My Aphorisms - http://www.shlomifish.org/humour.html
>
> God gave us two eyes and ten fingers so we will type five times as much as we
> read.
>
>
>
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Received on Mon May 04 2009 - 12:23:12 IDT