1. ## Distance measurement problem

Need help for this one too:

Consider a square whose side has length 1. Suppose S is an arbitrarily chosen set of 5 distinct points from this square. Prove that S contains two points whose distance is at most 1/root 2.

What will be the best way to answer such kind of question?

2. Originally Posted by faisalnet5
Need help for this one too:

Consider a square whose side has length 1. Suppose S is an arbitrarily chosen set of 5 distinct points from this square. Prove that S contains two points whose distance is at most 1/root 2.
Divide the unit square into for congruent subsquares.
How far apart can any two points within one of those subsquares be?
Use the pigeon-hole principle.

3. Thanks....but can u please tell me a bit more about how to use Pigeon-hole principle in this aspects?

Regards

4. Originally Posted by faisalnet5
Thanks....but can u please tell me a bit more about how to use Pigeon-hole principle in this aspects?
If you have five points(pigeons) and only four squares(Pigeon-holes), then one hole has two pigeons in it.