Problem # 9
Consider any 5 points all of which are in, or on , a square of side 1 . Prove that there must be at least one pair of them who will be no further than 22 apart.
THANKS FOR THE HELP
The 22 should be sqrt(2)/2.
Let me explain. Partition the square into 4 smaller squares by drawing two lines down the middles. Now there are 5 point being placed into 4 boxes. Pigeonholing we get 2 points are the same smaller square. The maximum distance from those two points is sqrt(2)/2.