MathDB

A regular triangle has side length

n{}

. We divided its sides into

n{}

equal parts and drew a line segment parallel with each side through the dividing points. A lattice of

1+2+\ldots+(n+1)

intersection points is thus formed. For which positive integers

n{}

can this lattice be partitioned into triplets of points which are the vertices of a regular triangle of side length

1

?
Proposed by Alexander Gunning, Cambridge, UK

Problem Statement