Selfridge–Conway procedure

Without loss of generality, we can write (see illustration above): In the following analysis "largest" means "largest according to that player": Note that if all we want is an envy-free division for a part of the cake (i.e. we allow free disposal), then we only need to use the first part of the Selfridge–Conway procedure, i.e.: This guarantees that there is no envy.

This procedure can be generalized to 4 partners in the following way:[3] This guarantees that there is no envy.

By induction, the procedure can be generalized to n partners, the first one dividing the cake to

equal pieces and the other partners follow by trimming.

By doing so an infinite number of times, we get an envy-free division of the entire cake.