Selfridge-Conway Method for 3 Players


Suppose we have a cake to divide among 3 people:

How can we divide it envy-free in a finite number of steps?

Can you divide the cake into three pieces distribute the pieces among three players, the union of the pieces (when put together) may not be the whole cake, and yet each individual will think he or she got the piece that is at least tied for largest piece? How can this be done?