Answer :
If it were not for the Abbot's conditions that the
number of
guests in
any room may not exceed three, and that every room must be occupied, it
would have been possible to accommodate either 24, 27, 30, 33, 36, 39,
or
42 pilgrims.
But to accommodate 24 pilgrims so that there shall be
twice
as many sleeping on the upper floor as on the lower floor, and eleven
persons on each side of the building, it will be found necessary to
leave
some of the rooms empty.
If, on the other hand, we try to put up 33,
36,
39 or 42 pilgrims, we shall find that in every case we are obliged to
place more than three persons in some of the rooms.
Thus we know that
the
number of pilgrims originally announced (whom, it will be remembered,
it
was possible to accommodate under the
conditions of the Abbot) must have
been 27, and that, since three more than this number were actually
provided with beds, the total number of pilgrims was 30.
The
accompanying
diagram shows how they might be arranged, and if in each instance we
regard the upper floor as placed above the lower one, it will be seen
that there are eleven persons on each side of the building, and twice
as
many above as below.
