Looney Labs Icehouse Mailing list Archive

Re: [Icehouse] volcano solitaire

  • FromMike Cowper <mcowper@xxxxxxxxxxxxxx>
  • DateSat, 21 Mar 2009 22:50:32 -0400
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.


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...

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><> Mike "Mr. Wizard" Cowper | http://www.wizardslab.net/~mcowper <>< ><> mcowper@xxxxxxxxxxxxxx --+-- Callsign: KC9BYV <> MIB#: 2001 <>< "Imagination is more important | "Any sufficiently advanced technology is than knowledge." A. Einstein | indistinguishable from magic." A. Clarke
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