10 entertaining tasks to warm up the brain
Recreation / / December 19, 2019
Try to solve the puzzle by Raymond Raymond Smullyan, mathematician and author of several collections of logic problems.
1. Money paradox
Richard and Paul have the same amount of money. How Richard to give the floor to have that was $ 10 more than he?
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Answer: 5 dollars. Many meet the $ 10 and make a mistake. Assume that each friend has a 50 dollars. If Richard will give $ 10 to Paul, then Paul would be $ 60, and Richard only 40. Hence, Paul will be $ 20 more than Richard, and not 10.
2. The slope of the roof
The roof of the house is asymmetrical: it is a ramp with the horizontal angle of 60 degrees, the other - the angle of 70 degrees. Suppose that a rooster lays an egg on the ridge of the roof. Where does it fall: toward a more gentle or steep slope?
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In any: roosters do not lay eggs.
3. Price of wine
A bottle of wine costs $ 10. The wine is $ 9 more expensive bottles. How much does an empty bottle?
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Answer: 0.5 dollar or 50 cents. Many meet the $ 1, but this is not true. If the bottle is really cost so much, then its contents shall be 9 dollars more - $ 10. So, along with the wine bottle would cost 11 dollars. And if the bottle is worth 0.5 dollars, wine - 9.5, then all together just $ 10.
4. enterprising merchant
The trader has bought goods for $ 7, sold it for 8, then re-bought for 9 and again sold it for 10. How much did he get?
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Answer: $ 2. Let us assume that a trader has $ 100, and during the day he will make only four described transaction.
First, he will pay for his purchase of $ 7, then he will be 93. When he sells his purchase of 8, he will have $ 101.
He went on to re-buy the same thing for $ 9, that is, again, spend $ 9 to buy, with the result that it is still $ 92. Finally, he sells item 10, and hence it will have $ 102.
5. Treadmill
To crawl on the treadmill stadium clockwise cochlea is required half an hour. When the snail crawls along the same track counterclockwise, the full circle takes 90 minutes. The results explain the discrepancy?
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No mismatch: a half hour in length do not differ from the 90 minutes.
6. Large and small birds
In pet stores sell large and small birds. Big Bird twice the price a little. The woman bought five large and three small birds. If she had instead bought three large and five small birds, they would have spent $ 20 less. How much does each bird?
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The price of one large bird is equal to the price of two small, so five big birds will cost as much as 10 small. So, five large and three small birds will cost as much as 13 smaller ones. On the other hand, the price of three large and five small birds is equal to the price of 11 children.
Thus, the difference between the price of five large and three small birds is equal to the difference between the price of 13 and 11 small birds, that is equal to the price of two young Since two small birds cost $ 20, the price of one such equal to 10 dollars.
Consequently, the expense to pay for the five large and three small birds will be $ 130. If a woman bought three large and five small birds, it would have spent 110 dollars, that is actually 20 less.
Answer: a small bird costs $ 10, most - 20.
7. The problem of the ten Darlings
Ten dogs and cats fed 56 biscuits. Each dog has got six biscuits, each cat - five. There were many dogs and many cats?
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There is a solution to this problem, which does not need any algebra or sorting options. First, feed each of the ten animals for five biscuits. Remain six biscuits. But now all the cats got their due share! Hence, the six remaining biscuits intended to dogs. And since every dog should get more of a biscuit, it means that the dogs - six and cats - four.
This solution is easy to check. If six dogs eat six biscuits, it goes 36 pieces. Four dogs, each of which is satisfied by five wafers, biscuits 20 eat. In sum, it will make 56 biscuits.
Answer: four cats and six dogs.
8. mysterious egg
How to say "I do not see the white yolk 'or' white yolk"?
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It would be better to say that the yolk yellow.
9. Plain colored socks
In a dark room is a wardrobe, in a box which are 24 red and 24 blue socks. What is the smallest number of socks you need to take out of the box, so that one could be at least one pair of socks of the same color?
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Answer: three sock. If you take out of the box three sock, then they are either all be the same color or two socks are the same color, and the third toe of another, which will also make a pair of single-color socks.
10. The question of international law
Suppose that on the border between the United States and Canada, there was a plane crash. Which of the two countries should be buried surviving passengers?
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It is hardly necessary to bury those who survived the plane crash.
Riddles for this collection are taken from the books of Raymond Raymond Smullyan The Lady or the Tiger? And Other Logic Puzzles and What Is the Name of This Book? The Riddle of Dracula and Other Logical Puzzles.
How did you manage to solve the puzzles? Tell me in the comments!
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