SOLUTIONS
\8.—The Monk's Puzzle.
The Monk might have placed dogs in the kennels in two
thousand nine hundred and twenty-six different ways, so that there
should be ten dogs on every side. The number of dogs might vary
from twenty to forty, and as long as the Monk kept his animals
within these limits the thing was always possible.
19.—
The Puzzle of the Prioress.
The Abbot of Chertsey was quite correct. The curiously-
shaped cross may be cut into four pieces that will fit together and
form a perfect square. How this is done is shown in the
illustration.
20.—
The Puzzle of the Doctor of Physic.
Here we have indeed a knotty problem. Our text-books tell us
that all spheres are similar, and that similar solids are as the cubes of
corresponding lengths. Therefore, as the circumferences of the two
phials were one foot and two feet respectively and the cubes of one
and two added together make nine, what we have to find is two
other numbers whose cubes added together make nine. These
numbers clearly must be fractional. Now, this little question has
really engaged the attention of learned men for two hundred and
fifty years, but although Peter de Fermat showed in the seventeenth
century how an answer may be found in two fractions with a
denominator of no fewer than twenty-one figures, not only are all
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