  The purpose of this paper is to introduce the idea of triangular Ramsey
numbers and provide values as well as upper and lower bounds for them. To do
this, the combinatorial game Mines is introduced; after some necessary theorems
about triangular sets are proved. This game is easy enough that young children
are able to play. The most basic variations of this game are analyzed and
theorems about winning strategies and the existence of draws are proved. The
game of Mines is then used to define triangular Ramsey numbers. Lower bounds
are found for these triangular Ramsey numbers using the probabilistic method
and the theorems about triangular sets.
