Just For Fun: Cake Problems

I was thinking about the variety of cake problems that are open-ended, accessible, and that encourage mathematical thinking and reasoning.

Easy: How to cut a cylindrical cake, Salvadoran-style, into n equal pieces.

Medium: How to cut a circular cake using 2 parallel cuts, such that each of the 3 resulting pieces has the same volume. 

Medium: How to cut a square cake into n pieces, so that each piece has the same amount of cake and same amount of frosting.  

Hard: How to cut a cake that already has a hole in it into 2 equal parts (from PCMI's pizza session, originally from Car Talk Puzzler). The PCMI version of the problem contains a diagram, so I give it to you here. Note that you don't know the sizes of the rectangles nor the relative angle of rotation of the inner rectangle.

Expert: How to cut a cake while maintaining maximum freshness.

Random Puzzler: How can you cut a cylindrical cake 3 times to make 8 equally large slices? 

Yum, cake! Lots of math fun in sharing things!