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?

o--------+--------o The distance between the closest
|A       |      B | should be 50*SQRT(13) feet, id  
|        |        | est, approximately 180.2775638 
+--------o--------+ feet. The distances between
|        |C       | friends would then be:
|        |        | A&B:300          A&C:50*SQRT(13)
o--------+--------o A&D:200          A&E:100*SQR(13)
|D       |       E| A&F:150*SQRT(5)  B&C:50*SQRT(13)
|        |        | B&D:100*SQRT(13) B&E:200
+--------o--------+ B&F:150*SQRT(5)  C&D:50*SQRT(13)
          F         C&E:50*SQRT(13)  C&F:200
                    D&E:300          D&F:50*SQRT(13)
                    E&F:50*SQRT(13)
                             

Posted by Dej Mar on 2010-08-06 10:20:53