MathDB

Dima has red and blue felt—tip pens, with one of them he paints rational points on the numerical axis, and with the other - irrational ones. Dima colored

100

rational and

100

irrational points, after which he erased the signatures that allowed to find out where the origin was and what the scale was. Sergey has a compass with which he can measure the distance between any two colored points

A

and

B

, and then mark on the axis a point located at a measured distance from any colored point

C

(left or right); at the same time, Dima immediately paints it with the appropriate felt-tip pen. How Sergei can find out what color Dima paints rational points and what color he paints irrational ones?

Problem Statement