with 12, and
the other numbers may remain unmoved. In every instance there must be an
even number in the central place, and any such number from 2 to 18 may
occur. Every solution has its complementary. Thus, if for every number in
the accompanying drawing we substitute the difference between it and 20,
we get the solution in the case of 37. Similarly, from the arrangement in
the original drawing, we may at once obtain a solution for the case of
38.

[Illustration]

36.--_The Donjon Keep Window._

In this case Sir Hugh had greatly perplexed his chief builder by
demanding that he should make a window measuring one foot on every side
and divided by bars into eight lights, having all their sides equal. The
illustration will show how this was to be done. It will be seen that if
each side of the window measures one foot, then each of the eight
triangular lights is six inches on every side.

"Of a truth, master builder," said De Fortibus slyly to the architect, "I
did not tell thee that the window must be square, as it is most certain
it never could be."

37.--_The Crescent and the Cross._

"By the toes of St. Moden," exclaimed Sir Hugh de Fortibus when this
puzzle was brought up, "my poor wit hath never shaped a more cunning
artifice or any more bewitching to look upon. It came to me as in a
vision, and ofttimes have I marvelled at the thing, seeing its exceeding
difficulty. My masters and kinsmen, it is done in this wise."

[Illustration]

The worthy knight then pointed out that the crescent was of a particular
and somewhat irregular form--the two distances _a_ to _b_ and _c_ to _d_
being straight lines, and the arcs _ac_ and _bd_ being precisely similar.
He showed that if the cuts be made as in Figure 1, the four pieces will
fit together and form a perfect square, as shown in Figure 2, if we there
only regard the three curved lines. By now making the straight cuts also
shown in Figure 2, we get the ten pieces that fit together, as in Figure
3, and form a perfectly symmetrical Greek cross. The proportions of the
crescent and the cross in the original illustration were correct, and
the solution can be demonstrated to be absolutely exact and not merely
approximate.

I have a solution in considerably fewer pieces, but it is far more
difficult to understand than the above method, in which the problem is
simplified by introducing the intermediate square.

38.--_The Amulet._

The puzzle was to plac