Euler Project problem 18: Find the max sum path of a triangle from top to bottom:

I've been studying this particular Euler problem for some time now, but without a background in dynamic programming and greedy algorithms (yet) I can't quite understand why nobody uses a top-down approach.

My professor posed this question to us, asking us to design an algorithm to find the max sum path in a triangle from top to bottom. Can any of you help me design an algorithm to find this sum without using exhaustive (brute force) search? It also cannot be a bottom-up approach either for what it's worth. A simple 2d array example would be fine, no need to read from a file or anything. Thanks!

Some positive integers are arranged in a triangle like the one shown in Figure below. Design an algorithm (more efficient than an exhaustive search, of course) to find the largest sum in a descent from its apex to the base through a sequence of adjacent numbers, one number per each level. 2 4 3 4 1 6 6