I found Jim Propp's idea of generalizing a problem to irrational numbers very interesting. So can this be done for the fummin problem? Hmm. Suppose we have N unit-circumference circles that we want to distribute evenly among K recipients. Then the "(N,K) fummin problem" is to find the smallest number f(N,K) of pieces that can be rearranged to give each recipient a total length of N/K. The *stable* fummin problem tries to find the limit s(N,K) = lim (1/m)f(mN,mK), m—>oo if it exists. (Question: Does s(N,K) <> f(N,K) for some (N,K) ?) Clearly s(N,K) depends only on the ratio N/K so by abuse of notation we define s(N/K) = s(N,K). Let alpha be a positive real number. Then the "generalized stable fummin problem" is to find the limit g(alpha) = lim s(N_j / K_j), j—>oo where N_j / K_j is a sequence of rational numbers converging to alpha, *if* the limit exists and is independent of the sequence N_j / K_j approaching alpha. Question: Is g(alpha) defined for any (all?) irrational numbers alpha > 0 ??? —Dan