The plan considers $51$ points of integer coordinates, so that the distances between any two points are natural numbers. Show that at least $49\%$ of the distances are even.
Source: 2010 Romania JBMO TST 4.4
Tags: lattice, combinatorics, combinatorial geometry
The plan considers $51$ points of integer coordinates, so that the distances between any two points are natural numbers. Show that at least $49\%$ of the distances are even.