MathDB

In a regular polygon with 100 vertices, 10 vertices are painted blue, and 10 other vertices are painted red.
1. Prove that there exist two distinct blue vertices

A_1

and

A_2

, and two distinct red vertices

R_1

and

R_2

, such that the distance between

A_1

and

R_1

is equal to the distance between

A_2

and

R_2

.
2. Prove that there exist two distinct blue vertices

A_1

and

A_2

, and two distinct red vertices

R_1

and

R_2

, such that the distance between

A_1

and

A_2

is equal to the distance between

R_1

and

R_2

Problem Statement