Let S = {(a, b) in R \times R | 0 <= a <= 1, 0 <= b <= 1}. Prove: If s1, s2, s3, s4, s5 in S are distinct,
then there exist 1 <= i 6 = j <= 5 such that the distance between si and sj is less than or equal
to √2/2.
Hint: Use the Pigeonhole Principle.