  We study the discrete variation of the classical cake-cutting problem where n
players divide a 1-dimensional cake with exactly (n-1) cuts, replacing the
continuous, infinitely divisible "cake" with a necklace of discrete,
indivisible "beads." We focus specifically on envy-free divisions, exploring
different constraints on player-preferences. We show we usually cannot
guarantee an envy-free division and consider situations where we can obtain an
envy-free division for relatively small. We also prove a 2-dimensional result
with a grid of indivisible objects. This may be viewed as a way to divide a
state with indivisible districts among a set of constituents, producing
somewhat gerrymandered regions that form an envy-free division of the state.
