Erich Friedman noticed a nice reciprocity between m and n: if we let S(m,n) denote the size of the smallest piece when m muffins are split among n noshers, then nS(m,n) = mS(n,m). So, for instance, Rich's observation that S(4,7) is at least 5/21 implies reciprocally that S(7,4) is at least 5/12. It has a really nice proof (maybe the problem should be submitted as a Quickie to the Monthly):  Hint: Instead of muffins, use sticks.  If you break m equal-length sticks into pieces that can be reassembled to form n equal-length sticks, then it's easy to take those n sticks and re-reassemble them to form m equal-length sticks: just use the breaks you've already made! Jim