The Canterbury Puzzles, and Other Curious ProblemsDudeney, Henry Ernest
Science
The Canterbury Puzzles, and Other Curious Problems
Dudeney, Henry Ernest
Puzzles; Riddles
Sir Isaac Newton has shown us, in his _Universal Arithmetic_, that we may
divide the bullocks in each case in two parts--one part to eat the
increase, and the other the accumulated grass. The first will vary
directly as the size of the field, and will not depend on the time; the
second part will also vary directly as the size of the field, and in
addition inversely with the time. We find from the farmer's statements
that 6 bullocks keep down the growth in a 10-acre field, and 6 bullocks
eat the grass on 10 acres in 16 weeks. Therefore, if 6 bullocks keep down
the growth on 10 acres, 24 will keep down the growth on 40 acres.
Again, we find that if 6 bullocks eat the accumulated grass on 10 acres
in 16 weeks, then
12 eat the grass on 10 acres in 8 weeks,
48 " " 40 " 8 "
192 " " 40 " 2 "
64 " " 40 " 6 "
Add the two results together (24 + 64), and we find that 88 oxen may be
fed on a 40-acre meadow for 6 weeks, the grass growing regularly all the
time.
112.--_The Great Grangemoor Mystery._
We were told that the bullet that killed Mr. Stanton Mowbray struck the
very centre of the clock face and instantly welded together the hour,
minute, and second hands, so that all revolved in one piece. The puzzle
was to tell from the fixed relative positions of the three hands the
exact time when the pistol was fired.
We were also told, and the illustration of the clock face bore out the
statement, that the hour and minute hands were exactly twenty divisions
apart, "the third of the circumference of the dial." Now, there are
eleven times in twelve hours when the hour hand is exactly twenty
divisions ahead of the minute hand, and eleven times when the minute hand
is exactly twenty divisions ahead of the hour hand. The illustration
showed that we had only to consider the former case. If we start at four
o'clock, and keep on adding 1 h. 5 m. 27-3/11 sec., we shall get all
these eleven times, the last being 2 h. 54 min. 32-8/11 sec. Another
addition brings us back to four o'clock. If we now examine the clock
face, we shall find that the seconds hand is nearly twenty-two divisions
behind the minute hand, and if we look at all our eleven times we shall
find that only in the last case given above is the seconds hand at this
distance. Therefore the shot must have been fired at 2 h. 54 min. 32-8/11
sec. exactly, or, put the other way, at 5 min. 27-3/11 sec. to three
o'clock. This is the correct and only possible answer to the puzzle.
113.--_Cutting a Wood Block._
Though the cubic contents are sufficient for twenty-five pieces, only
twenty-four can actually be cut from the block. First reduce the length
of the block by half an inch. The smaller piece cut off constitutes the
portion that cannot be used. Cut the larger piece into three slabs, each
one and a quarter inch thick, and it will be found that eight blocks may
easily be cut out of each slab without any further waste.
Public-domain text, read in full here on John Shaqi.
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