You can determine whether one box can fit in another in constant time. That's all you really need to know to to solve the problem in polynomial time. It's meant to be open ended, though there is a particularly efficient method for solving the problem.

<r>I was reminded of this problem by the problem here (<URL url="http://www.wilmott.com/messageview.cfm?catid=26&threadid=70684"><LINK_TEXT text="http://www.wilmott.com/messageview.cfm? ... adid=70684">http://www.wilmott.com/messageview.cfm?catid=26&threadid=70684</LINK_TEXT></URL>) but this...

<t>You can also solve the probability of the Markov chain explicitly using matrix notation. We can define an initial distribution m, and a transition probability to matrix P to represent the evolution of the sum from dice roll to dice roll. The problem's state space is the values {0,1,2,...,20}.Defi...