STEALING THE BELL-ROPES.
(
Patchwork Puzzles)
Two men broke into a church tower one night to steal the bell-ropes. The
two ropes passed through holes in the wooden ceiling high above them,
and they lost no time in climbing to the top. Then one man drew his
knife and cut the rope above his head, in consequence of which he fell
to the floor and was badly injured. His fellow-thief called out that it
served him right for being such a fool. He said that he should have done
as he was doing, upon which he cut the rope below the place at which he
held on. Then, to his dismay, he found that he was in no better plight,
for, after hanging on as long as his strength lasted, he was compelled
to let go and fall beside his comrade. Here they were both found the
next morning with their limbs broken. How far did they fall? One of the
ropes when they found it was just touching the floor, and when you
pulled the end to the wall, keeping the rope taut, it touched a point
just three inches above the floor, and the wall was four feet from the
rope when it hung at rest. How long was the rope from floor to ceiling?
Answer:
Whenever we have one side (a) of a right-angled triangle, and know the
difference between the second side and the hypotenuse (which difference
we will call b), then the length of the hypotenuse will be
a squared b
--- + -.
2b 2
In the case of our puzzle this will be
48 x 48
------- + 11/2 in. = 32 ft. 11/2 in.,
6
which is the length of the rope.
180-- THE FOUR SONS.
The diagram shows the most equitable division of the land possible, "so
that each son shall receive land of exactly the same area and exactly
similar in shape," and so that each shall have access to the well in
the centre without trespass on another's land. The conditions do not
require that each son's land shall be in one piece, but it is necessary
that the two portions assigned to an individual should be kept apart, or
two adjoining portions might be held to be one piece, in which case the
condition as to shape would have to be broken. At present there is only
one shape for each piece of land--half a square divided diagonally. And
A, B, C, and D can each reach their land from the outside, and have each
equal access to the well in the centre.
