From any letter in the diagram, a move can only be made to a letter diagonally adjacent and below. In how many different ways can a path that spells MATHCOUNTS be taken?
There are 2^4 ways to get to the Cs, and thinking backwards, we see that there are 2^4 ways to get from the Cs to the S. So there are 2^4*2^4 = 256 ways.
