PARADOXES by K2V (Bill Jowitt)
An old man once said to me, "I ALWAYS tell lies." Could I believe
him?
Such seeming paradoxes intrigue me, and so I look for them. Here
are one or a few for you to think about. (Well, there is not one
only, and if I can count, it is not correct to say two.).
They can show up our "cock-eyed" thinking. For instance, we all
know that it is criminal to drink and drive. The Ministry of
Transport figures show that one third of the deaths on the road are
caused by drunken drivers. This means that two thirds of the
deaths, that is, twice as many, are caused by sober drivers. Would
the road deaths be reduced if all drivers were drunk?
Seven men once arrived at a lonely, spooky, highland hotel and asked
for accommodation for the night, all wanting separate rooms. The
manager admitted that he only had six rooms left, but thought he
would be able to fix them up. He took the first man to Room 1, and
asked the next man to stay there for a few minutes. He then took
the third man to Room 2, the fourth man to Room 3, the fifth man to
Room 4, and the sixth man to Room 5. He then returned to the first
room, and asked the seventh man to follow him to Room 6. All taken
care of??
Three men had dinner at a hotel and got the bill amounting to #30.
They each gave the waiter #10. He took the money to the office,
where he was told that there had been a mistake; the bill should
have been #25, and he was given #5 change to return to the men. On
the way back he realised that it would be difficult to divide the #5
between the three men, that the men did not know the correct amount,
and would be glad of any refund. So he kept #2 and returned #1 to
each of the three men. That is, the three men had paid #9 each,
making #27 and the waiter had put #2 in his pocket. #27 plus #2
makes #29, but the men originally handed over #30. Where has the
other #1 gone?
Many years ago a wealthy Arab, in his will, left seventeen beautiful
horses to his three sons. He stated that the eldest son was to have
one half of the horses, the next son one third, and the youngest,
one ninth. They obviously could not divide the horses as their
father wished, without chopping some to pieces. They finally asked
the advice of a wise old man. He arrived at the stable with his own
old horse and placed it with the other seventeen. He then began to
share the eighteen horses. The eldest son took one half of the
eighteen, nine; the next, one third, six; and the youngest, one
ninth, two. Nine plus six plus two make seventeen, and the wise old
man was left with his own horse. How did he do it?
If a metal band were put round the Equator, what length would have
to be let in to lift the band by one half inch all the way round the
Earth?
Answer: Three & 1/7 inches
If a metal band were put round a jam jar, what length would have to
be let in to lift the band by one half inch all the way round the
jar.
Answer: Three & 1/7 inches
Any two circles with a difference of one unit in diameters will have
approx. three and one-seventh units difference in circumferences.
There are 10 posts in a straight line, 10 metres apart. What is the
distance between the first and last post?
Answer: Ninety metres
A clock strikes six in five seconds. How long does it take to
strike twelve?
Answer: Eleven seconds
A bottle and a cork costs together 22p. The bottle costs 20p more
than the cork. How much does the bottle cost?
Answer: Twenty-one pence
A farmer's wife took some eggs to market. To her first customer she
sold half her stock of eggs and half an egg. To her second customer
she sold half the remainder and half an egg. Then to her third and
last customer she sold half of her remaining eggs and half an egg.
She was left with three eggs, but during her three transactions she
had broken no eggs. How many eggs did she start with?
Answer: Thirty-one
I have a glass containing some liquid A. In another glass I have an
equal amount of liquid B. I now take one measure of liquid A and
pour it into liquid B, stir it up, then take the same measure of the
mixture from B and pour it into liquid A. Now is there more A in B
than B in A?
Would the answer be the same if the mixture was NOT stirred; or, if
the original amounts of the two liquids were NOT equal?
Answer: Equal amounts, in all
cases.
We have two parents, four grand-parents, eight great-grand-parents.
How many ancestors have we got at twenty generations (say, six
hundred years) back?
Answer: 1,048,576! Are we
related?
Mathematically related to the puzzle above are these two.
If a person sent a chain letter to two friends and each of them sent
a letter to two friends, and so on, what is the minimum number of
sets of letters that would have to be sent so that every man, women
and child on Earth would receive only one letter?
Answer: Thirty sets.
If we took a thin sheet of paper, one-thousandth of an inch thick,
(0.025mm), tore it in half and placed one half on top of the other,
and then tore the pile in half and piled them again, how high would
the pile be after fifty times?
Answer: Seventeen million+ miles!
(Twentyseven million+kilometres)
If you do not believe the last answer, take a sheet of newspaper and
see how many times you can do the same with it.
It takes half an hour to dry half a dozen tea-towels on the line.
How long does it take to dry one dozen?
Answer: Half an hour
There are three volumes, each of 500 pages, placed in order on a
shelf. A bookworm starts to eat its way through from page 1, volume
1 to page 500, volume 3. How many pages does it eat through?
Answer: Five hundred pages