MathDB

Is it possible in a plane mark

10

red,

10

blue and

10

green points (all distinct) such that three conditions hold:

i)

For every red point

A

there exists a blue point closer to point

A

than any other green point

ii)

For every blue point

B

there exists a green point closer to point

B

than any other red point

iii)

For every green point

C

there exists a red point closer to point

C

than any other blue point

Problem Statement