\magnification=1200 \hsize=4in \overfullrule=0pt \input amssym %\def\frac#1 #2 {{#1\over #2}} \def\emph#1{{\it #1}} \def\em{\it} \nopagenumbers \noindent % % {\bf Walter Stromquist} % % \medskip \noindent % % {\bf Envy-Free Cake Divisions Cannot be Found by Finite Protocols} % % \vskip 5mm \noindent % % % % We show that no finite protocol (even if unbounded) can guarantee an envy-free division of a cake among three or more players, if each player is to receive a single connected piece. \bye .