\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} a) Two students are sharing a loaf of
bread. Student Alpha eats half of the loaf, then student Beta eats
half of what remains, then Alpha eats half of what remains, and so
on. How much of the loaf will each student eat?

\medskip

\noindent b) Two students are sharing a loaf of bread. Student Alpha,
now hungrier and more ferocious, eats two-thirds of the loaf, then
student Beta eats eats half of what remains, then Alpha eats
two-thirds of what remains, then Beta eats half of what remains, and
so on. How much of the loaf will each student eat?

\medskip

\noindent c) Now start with three students: Alpha, Beta, and
Gamma. They decide to share a loaf of bread. Alpha eats half of the
loaf, passes what remains to Beta who eats half, and then on to
Gamma who eats half, and then back to Alpha who eats half, and so
on. How much of the loaf will each student eat?

\vfil\eject\end