Triangular Numbers and CombinatoricsThe triangular number, $$T^2_n$$, is found by counting the number of packed circles forming the equilateral triangle with $$n$$ circles to a side. It is well-known that $$T^2_n = n(n+1)/2$$, which happens to be the number of ways that 2 objects can be selected from among $$n+1$$ objects. We explore this connection between combinatorics, the triangular numbers, and their higher-dimensional analogs. Project EulerSolutions and discussions of the Project Euler problems. These are a collection of increasingly challenging mathematical and computational exercises across the field of number theory. This is a work in progress and I will post new solutions as I solve them.