MathDB

Cardinality of set of lattice points with different pairwise

Source: India Postals 2015

November 15, 2015

analytic geometrycombinatorics

Problem Statement

Let

S

be a set of in

3-

space such that each of the points in

S

has integer coordinates

(x,y,z)

with

1 \le x,y,z \le n

. Suppose the pairwise distances between these points are all distinct. Prove that

|S| \le min \{(n+2)\sqrt{\frac{n}{3}},n\sqrt{6} \}