Problem

Source:

Tags: combinatorics



An infinite triangular lattice is given, such that the distance between any two adjacent points is always equal to $1$. Points $A$, $B$, and $C$ are chosen on the lattice such that they are the vertices of an equilateral triangle of side length $L$, and the sides of $ABC$ contain no points from the lattice. Prove that, inside triangle $ABC$, there are exactly $\frac{L^2-1}{2}$ points from the lattice.


Attachments: