Six friends were playing a game of indoor soccer together, but got into a fight during their game. Upset with each other, they decided to position themselves in the (square) 300x300 foot gymnasium so as to maximize the distance between the closest pair. Where should they each stand?

(In reply to Better Still by bernie)

Nice job, Bernie! Wish I had thought of it.

It occurs to me that an instinctive way to solve this puzzle is to imagine six mutually repellent specks in a box.  If I started with my solution and shook the box, would I expect the specks to come back to their starting position, or would they end up in a different position that had greater inherent stability?  My gut tells me they would end up with your configuration, where a second speck has wedged itself into a corner...

Posted by Bryan on 2004-08-18 12:03:09