SOLUTIONS
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 place your pencil on the A at the top of the
amulet and count in how many different ways you could trace out
the word "Abracadabra" downwards, always passing from a letter
to an adjoining one.
A
B B
R R R
A A A A
C C C C C
A A A A A A
D D D D D D D
AAAAAAAA
BBBBBBBBB
RRRRRRRRRR
AAAAAAAAAAA
" Now, mark ye, fine fellows," said Sir Hugh to some who had
besought him to explain, " that at the very first start there be two
ways open : whichever B ye select there will be two several ways
of proceeding (twice times two are four) ; whichever R ye select
there be two ways of going on (twice times four are eight) ; and so
on until the end. Each letter in order from A downwards may so
be reached in 2, 4, 8, 16, 32, etc., ways. Therefore, as there be
ten lines or steps in all from A to the bottom, all ye need do is to
multiply ten 2's together and truly the result, 1,024, is the answer
thou dost seek."
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