MathDB

Let regular hexagon is divided into

6n^2

regular triangles. Let

2n

coins are put in different triangles such, that no any two coins lie on the same layer (layer is area between two consecutive parallel lines). Let also triangles are painted like on the chess board. Prove that exactly

n

coins lie on black triangles. https://cdn.artofproblemsolving.com/attachments/0/4/96503a10351b0dc38b611c6ee6eb945b5ed1d9.png

Problem Statement