There is a decagon with eight 150 degree angles and two 120 degree angles. The lengths of its sides are a set of ten consecutive integers. Maximize the length of its longest side.

... that took me a long time to think up, but you probably thought it in a second.

The longer the sides get (still being consecutive integers), the closer the decagon gets to looking equilateralish.  Since two angles are 30 degrees smaller than the other eight, I would guess, as a first impression ball park estimate type of an arrangement, that the longest side is probably not longer than 20 units (and obviously not shorter than 10).

However, I have no proof, and I could be way off.  I guess I'll just have to wait for Charlie's answer.

Posted by Dustin on 2005-01-30 22:27:37