Hey I can't seem to formulate the DP for [this] ? (http://community.topcoder.com/stat?c=problem_statement&pm=13964&rd=16514&rm=326779&cr=10574855)

I understand that the solution space is reduced to 3^n as compared to 4^n, and that we have to work on individual digits of the sum, but I'm unable to grasp how to take care of the carry and how that would fit in the DP formulation ?