Let (m,n) be an ordered pair of positive integers. While m>0 and n>0, let k_1 be a random positive integer between 1 and m and k_2 a random positive integer between 1 and n. Output (k_1,k_2). Let m=m-k_1 and n=n-k_2. What is the expected number of outputs?
Note that in the one-dimensional version of the problem, starting with a single integer n, the expected number of outputs is the nth harmonic number 1+1/2+1/3+...+1/n.