Let's take another crack at this puzzler. If there is anyone
"out there" who is remotely interested in FreeCell solvers,
you have got to be concerned about the theoretical fanout
of FreeCell moves. Fanout needs to be restricted to the
minimum of necessary moves at each step. Investigating
every possible move is not only unnecessary, but it
guarantees that a solver cannot perform an exhaustive
search in any practical time.
Therefore, the purpose of this exercise is to discuss the
maximum fanout with the maximum of limitations, i.e.
never allowing an unnecessary move. Clearly, at certain
points, there are few or zero moves possible. At other
points there may be quite a few. However, a possible
move may not be a necessary move. For example, if
you try moving a card to one of 4 empty free cells, and
can't find a solution by doing so, moving it to one of
the other free cells does not need to be tried. This 2nd
move is unnecessary or redundant. There are many
such moves. This is essentially a discussion of them.
I can imagine that the proof that a move is redundant
could get to be quite complex, indeed.
So, again, what is the maximum NECESSARY
fanout given some constructed layout, such as the
one Shlomi proposes below (or one of your own
choosing)? I chose a layout with only one empty
free cell and one empty column to produce the
maximum of 41 moves that I came up with.
By the way, regarding Shlomi's layout below, I
calculate that there are zero NECESSARY moves.
The layout produces an immediate flourish!
It was a useful example to get the discussion
started, however. But no discussion occurred!
Is there anybody out there?
----- Original Message -----
From: "Gary Campbell" <gary_at_numin8r.us>
To: <fc-solve-discuss_at_yahoogroups.com>
Sent: Monday, May 04, 2009 1:21 PM
Subject: Re: A Puzzler for You
> 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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>>
>>
>>
>>
>
>
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>
Received on Wed May 13 2009 - 06:55:30 IDT