2017 blue points and 58 red points
Source: 2017 China TST 5 P3
April 8, 2017
combinatorics
Problem Statement
For a rational point (x,y), if xy is an integer that divided by 2 but not 3, color (x,y) red, if xy is an integer that divided by 3 but not 2, color (x,y) blue. Determine whether there is a line segment in the plane such that it contains exactly 2017 blue points and 58 red points.