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 Solution... by Arpan)

A regular hexagon with sides of 173.2 each, will be 346.4 feet from tip to tip and will not fit in the 300x300 room.

I propose placing one person in each of the four corners of the room, and then placing the remaining two along a centerline of the room that is parallel to two of the walls of the room, and equally distant from each of the other two walls. If they are about 164.575 feet apart, they will also be that distance from two corner people each, and that is the minimum distance, as the other distances are 300 feet.

Posted by Charlie on 2004-08-17 09:47:44