MathDB

The country of Harpland has three types of coins: green, white and orange. The unit of currency in Harpland is the shilling. Any coin is worth a positive integer number of shillings, but coins of the same color may be worth different amounts. A set of coins is stacked in the form of an equilateral triangle of side

n

coins, as shown below for the case of

n=6

.
[asy] size(100); for (int j=0; j<6; ++j) { for (int i=0; i<6-j; ++i) { draw(Circle((i+j/2,0.866j),0.5)); } } [/asy]
The stacking has the following properties:
(a) no coin touches another coin of the same color;
(b) the total worth, in shillings, of the coins lying on any line parallel to one of the sides of the triangle is divisible by by three.
Prove that the total worth in shillings of the green coins in the triangle is divisible by three.

Problem Statement