Convex hexagon ABCDEF is equiangular but has no two sides the same length. Its sides in some order are 1, 2, 3, 4, 5 and 6 units long. If AB=1 and CD>BC, what are the lengths of BC, CD, DE, EF and FA?

Another convex hexagon is also equiangular and has sided measuring 1, X, 3, 4, 5, and 6 units long in that order going clockwise. What is the measure of X?

I just happened to be looking at the "centrifugal balance problem" when I thought of another one of my crazy analogies.  This problem is exactly like centrifugal balance, with a six-slotted centrifuge, except the samples don't weigh the same (is this possible in the use of a real centrifuge?).

Now, I would place the samples like this:

 3 5
1   2
 6 4

Of course, that translates to the hexagon having sides (going clockwise) 1, 3, 5, 2, 4, 6.

Part 2 is rendered even simpler (in my crazy mind) by this analogy.

 8 3
1   4
 6 5

Posted by Tristan on 2004-10-16 01:27:54