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?

How about placing two in adjacent corners, a third in the center of the opposite wall, then toward the empty corners, and along the walls from the occupied corners place two more at 200 feet?  Then place the sixth in the middle of the rectangle formed by the first two and last two.  The distances to closest neighbors for each is either 200 feet or 180.27756...(50 radical 13, half the diagonal of the rectangle which is 200 feet by 300 feet). 

Posted by bernie on 2004-08-17 20:18:34