MathDB

An equilateral triangle

\mathcal{T}{}

with side 111 is divided by straight lines parallel to its sides into equilateral triangles with side 1. The vertices of these small triangles, except the centre of

\mathcal{T}{}

are marked. Call a set of several marked points linear if[*]the marked points lie on a line

\ell

parallel to one of the sides of the triangle

\mathcal{T}

and; [*]if two marked points on

\ell

are in this set, every other marked point inbetween them is in the set. How many ways are there to split all the marked points into 111 linear sets?

Problem Statement