Our logo represents a solution of the following problem:
THE CHEESE PROBLEM: Divide a disc into a
finite number of congruent pieces in such a
a way that not all of them contain the center.
Can you find other configurations with the same property? There are infinitely many such configurations. However, all known solutions (except for the one in the logo) have the property that the boundaries of all the pieces consist only of circular arcs of the same radius as the original circle. We do not know whether there is a partition of the disc into congruent pieces other than the logo such that not all pieces contain the center and not all boundaries are circle arcs.
Send your solution to:Prof. Svetlana Katok
Department of Mathematics
Penn State University
University Park, PA 16802
Update: see various solutions in the preprint by Joel Haddley and Stephen Worsley "Infinite families of monohedral disk tilings", arXiv:1512.03794.