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