(Please delete my e-mail address from any such documents before distributing them — thanks.) The multi-author muffin paper begins as follows: ----- You have m muffins and s students. You want to divide the muffins into pieces and give the shares to students such that every student has m muffins. Find a divide-and-distribute protocol that maximizes the minimum piece. ----- Apologies for not remembering whether I posted the following already, or merely thought it: Suppose we change the problem by changing the objective criterion, from maximizes the minimum piece. (the muffin problem) to minimizes the *number* of pieces (the fummin problem). (I think now I proposed this criterion for finding nice geometric dissections like regular polygon-to-regular polygon ones, but not for a muffin problem.) Minor simplification: Given M disjoint circles of unit circumference, What is the smallest number of pieces to chop them into that can be reassembled into S disjoint congruent circles? (Of course, each would have circumference M/S.) First question: What is the smallest case, if any, where the solution to this problem uses a different dissection from that used in the muffin problem for the same M and S ? —Dan