  There is a heterogeneous resource that contains both good parts and bad
parts, for example, a cake with some parts burnt, a land-estate with some parts
heavily taxed, or a chore with some parts fun to do. The resource has to be
divided fairly among $n$ agents with different preferences, each of whom has a
personal value-density function on the resource. The value-density functions
can accept any real value --- positive, negative or zero. Each agent should
receive a connected piece and no agent should envy another agent. We prove that
such a division exists for 3 agents and present preliminary positive results
for larger numbers of agents.
