THE CANTERBURY PUZZLES
96.—
The Fifteen Orchards.
The number must be the least common multiple of 1,2, 3, &c,
up to 15, that, when divided by 7, leaves the remainder 1, by 9
leaves 3, by 11 leaves 10, by 13 leaves 3, and by 14 leaves 8.
Such a number is 120. The next number is 360,480, but as we
have no record of a tree—especially a very young one—bearing
anything like such a large number of apples, we may take 120 to be
the only answer that is acceptable.
97.—
The Perplexed Plumber.
The rectangular closed cistern that shall hold a given quantity of
water and yet have the smallest possible surface of metal must be a
perfect cube—that is, a cistern every side of which is a square.
For 1,000 cubic feet of water the internal dimensions will be
10 ft. x 10 ft. x 10 ft., and the zinc required will be 600 square
feet. In the case of a cistern without a top the proportions will be
exactly half a cube. These are the "exact proportions" asked for
in the second case. The exact dimensions cannot be given, but
12*6 ft. x 12*6 ft. x 6*3 ft. is a close approximation. The cistern
will hold a little too much water, at which the buyer will not
complain, and it will involve the plumber in a trifling loss not worth
considering.
98.—
The Nelson Column.
If you take a sheet of paper and mark it with a diagonal line, as in
figure A, you will find that when you roll it into cylindrical form,
with the line outside, it will appear as in
F "71 f^f^
n
§
ure
B.
I
/ \ /
| It will be seen that the spiral (in one com-
U f
I plete turn) is merely the hypotenuse of a right-
\f
- . 1.13 angled triangle, of which the length and width
£ J LJ^J of the paper are the other two sides. In the
puzzle given, the lengths of the two sides
of the triangle are 40ft. (one-fifth of 200ft.) and 16ft. 8in. There-
fore the hypotenuse is 43ft. 4in. The length of the garland is
186
