1 2 3 4 5 6 7 8
THE CANTERBURY PUZZLES
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 clearly 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 Ih. 5m. 27 3-1 Isec, we shall get all these eleven times, the
last being 2h. 54min. 32 8-1 Isec. 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 2h. 54min. 32 8-1 Isec.
exactly, or, put the other way, at 5min. 27 3-1 Isec. 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.
114.—The Tramps and the Biscuits.
The smallest number of biscuits must have been 1021, from
which it is evident that they were of that miniature description that
194



Copyright © MyMathForum 2006