It is possible to get all but 1. As pointed out you do need to erupt
pieces other than the tops, just not capture them. It is even possible
to capture all but 1 and have all of the mediums and smalls back in
their original positions with the last large capture. It is further
possible to then capture all of the mediums except 1 without capturing
any of the smalls and with the smalls all back in their original
positions. I have not yet been able to capture all of the smalls after
that though. The best that I can do is get down to one large, one
medium and two smalls. One in each of the zones that Dale labeled. I
don't know if that's possible or not. I've not attempted, but thought
about, a further restriction that the pieces left all be the same
color. I may try that sometime.
Mike
On Mar 10, 2009, at 2:26 AM, Dale Newfield wrote:
David L. Willson wrote:
> The second is to capture all the large without capturing anything
> else. I couldn't get past 21 of 25. The 4 remaining in play seem
to
> be unable to meet, no matter what I do.
John Francis wrote:
I've been working on this problem myself for a while (off and on).
I'm thinking that there is a reason, a mathematical or algorithmic
reason, that there must be four pieces left and not three. I've
tried MANY times to resolve this problem, and have failed to
eliminate one of the four pieces.
I just realized the puzzle doesn't actually prevent you from having
more than the just the top pieces erupt, which could put a small or
medium on top of a large which would put that large in a different
orbit on subsequent eruption...
...but if you did attempt the puzzle with that restriction, it is
trivial to show that you can do no better than 4. The following
grid labels the 4 disjoint sets of board locations that can each be
made to jump onto one another. Meaning W's can be made to capture
W's, but not X's, Y's, or Z's. Likewise with the other large
labels. Therefore at least one large must be left in each orbit.
W X W X W
Y Z Y Z Y
W X W X W
Y Z Y Z Y
W X W X W
So it seems in order to do better than 21 you need to let eruptions
go farther that just the top piece, and use that to get the
"leftover" larges from the 4 orbits into other orbits so that they
can capture one another. Careful not to capture anything other than
a large, though...
-Dale
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><> Mike "Mr. Wizard" Cowper | http://www.wizardslab.net/~mcowper
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