MathDB

Every point in the plane was colored in red or blue. Prove that one the two following statements is true:

\bullet

there exist two red points at distance

1

from each other;

\bullet

there exist four blue points

B_1

B_2

B_3

B_4

such that the points

B_i

and

B_j

are at distance

|i - j|

from each other, for all integers

i

and

j

such as

1 \le i \le 4

and

1 \le j \le 4

Problem Statement