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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