Covering unit segments
Source: Serbia TST 2017 #4
May 22, 2017
combinatorics
Problem Statement
We have an square divided into unit squares. Each side of unit square is called unit segment. Some isoceles right triangles of hypotenuse are put on the square so all their vertices are also vertices of unit squares. For which it is possible that every unit segment belongs to exactly one triangle(unit segment belongs to a triangle even if it's on the border of the triangle)?