  We study the existence of fair distributions when we have more guests than
pieces to allocate, focusing on envy-free distributions among those who receive
a piece. The conditions on the demand from the guests can be weakened from
those of classic cake-cutting and rent-splitting results of Stromquist,
Woodall, and Su. We extend existing variations of the cake-cutting problem with
secretive guests and those that resist the removal of any sufficiently small
set of guests.
