Miscellaneous Puzzles 75- THE TOWER OF PISA
"When I was on a little tour in Italy, collecting material for my book on
Improvements in the Cultivation of Macaroni," said the Professor, "I happened
to be one day on the top of the Leaning Tower of Pisa, in company with an
American stranger. 'Some lean!' said my companion. 'I guess we can build a
bit straighter in the States. If one of our skyscrapers bent in this way there
would be a hunt round for the architect.'
"I remarked that the point at which we leant over was exactly 179 feet from
the ground, and he put to me this question: 'If an elastic ball was dropped
from here, and on each rebound rose exactly one-tenth of the height from
which it fell, can you say what distance the ball would travel before it came to
rest?' I found it a very interesting proposition."
- A MATCHBOARDING ORDER
A man gave an order for 297 ft. of match boarding of usual width and thick-
ness. There were to be sixteen pieces, all measuring an exact number of feet
-no fractions of a foot. He required eight pieces of the greatest length, the
remaining pieces to be I ft., 2 ft., or 3 ft. shorter than the greatest length.
How was the order carried out? Supposing the eight of greatest length were
15 ft. long, then the others must be made up of pieces of 14 ft., 13 ft., or 12 ft.
lengths, though every one of these three lengths need not be represented.
- GEOMETRICAL PROGRESSION
Professor Rackbrane proposed, one morning, that his friends should write
out a series of three or more different whole numbers in geometrical progres-
sion, starting from 1, so that the numbers should add up to a square. Thus,
1 + 2 + 4 + 8 + 16 + 32 = 63.
But this is just one short of bemg a square. I am only aware of two answers
in whole numbers, and these will be found easy to discover.- A PAVEMENT PUZZLE
Two square floors had to be paved with stones each I ft. square. The num-
ber of stones in both together was 2,120, but each side of one floor was 12 ft.