It occurred to me after Bill Gasarch's recent MIT Combinatorics Seminar talk that there's a problem related to the muffin problem that has just a single real parameter, which plays the same role as m/n but can be irrational; call it p (for portion). We have infinitely many muffins and infinitely many noshers. Each muffin gets divided into pieces, and each piece is given to one of the noshers, in such a fashion that each piece gets eaten and each nosher gets p muffins. Let F(p) be the infimum of the sizes of the pieces. What can we say about F(p)? For instance, is it periodic with period 1? Or could F(p+1) be smaller than F(p) for some p? Note that when p is rational, F(p) = inf f(m,n) over all pairs m,n with m/n = p. (Or is it? This seemed obvious when I wrote it, but now I’m not so sure. There are two inequalities in this claim, and right now I’m not seeing how to prove either of them.) Can anyone compute F(p) for some quadratic irrational p, such as (-1+sqrt(5))/2? (That's probably asking for too much; I can’t even determine F(2/n) for all odd n.) Jim Propp