"In the
prison
is a
switch room, which contains two light switches labeled A and B, each of
which
can be in either the 'on' or the 'off' position. I am not telling you
their
present positions. The switches are not connected to anything.
"After
today,
from
time to time whenever I feel so inclined, I will select one prisoner at
random
and escort him to the switch room. This prisoner will select one
of the
two switches and reverse its position. He must move one, but only
one of
the switches. He can't move both but he can't move none
either.
Then he'll be led back to his cell.
"No one
else
will
enter the switch room until I lead the next prisoner there, and he'll
be
instructed to do the same thing. I'm going to choose prisoners at
random. I may choose the same guy three times in a row, or I may
jump
around and come back.
"But,
given
enough
time, everyone will eventually visit the switch room as many times as
everyone
else. At any time anyone of you may declare to me, 'we have all visited
the
switch room' and be 100% sure.
"If it
is
true, then
you will all be set free. If it is false, and somebody has not
yet
visited the switch room, you will be fed to the alligators."