MathDB

4

Part of 2017 Serbia Team Selection Test

Problems(1)

Covering unit segments

Source: Serbia TST 2017 #4

5/22/2017
We have an n×nn \times n square divided into unit squares. Each side of unit square is called unit segment. Some isoceles right triangles of hypotenuse 22 are put on the square so all their vertices are also vertices of unit squares. For which nn 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)?
combinatorics