three are
more difficult to discover.

42.--_The Riddle of the Pilgrims._

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.

[Illustration]

43.--_The Riddle of the Tiled Hearth._

The correct answer is shown in the illustration on page 196. No tile is
in line (either horizontally, vertically, or diagonally) with another
tile of the same design, and only three plain tiles are used. If after
placing the four lions you fall into the error of placing four other
tiles of another pattern, instead of only three, you will be left with
four places that must be occupied by plain tiles. The secret consists in
placing four of one kind and only three of each of the others.

[Illustration]

44.--_The Riddle of the Sack of Wine._

The question was: Did Brother Benjamin take more wine from the bottle
than water from the jug? Or did he take more water from the jug than wine
from the bottle? He did neither. The same quantity of wine was
transferred from the bottle as water was taken from the jug. Let us
assume that the glass would hold a quarter of a pint. There was a pint of
wine in the bottle and a pint of water in the jug. After the first
manipulation the bottle contains three-quarters of a pint of wine, and
the jug one pint of water mixed with a quarter of a pint of wine. Now,
the second transaction cons