Distances between red dots
Source: Kvant Magazine No. 2 2020 M2591
March 10, 2023
combinatoricscombinatorial geometry
Problem Statement
There are 100 blue lines drawn on the plane, among which there are no parallel lines and no three of which pass through one point. The intersection points of the blue lines are marked in red. Could it happen that the distance between any two red dots lying on the same blue line is equal to an integer?From the folklore