Logic tasks. A Short Course in Logic: The Art of Right Thinking Peter Lied
Task Conditions
1. Each of the 10 bags contains 10 coins. Each coin weighs 10 g. But in one bag all the coins are counterfeit - not 10 g each, but 11 g each. How, using only one-time weighing, can you determine which bag contains counterfeit coins (all bags are numbered from 1 to 10)? The bags can be opened and any number of coins can be pulled out of each.
2. On all three iron cans with cookies, the labels are mixed up: “ Oatmeal cookies», « Shortbread and Chocolate Chip Cookies. The jars are closed, and you can only take one cookie from one (any) jar, and then arrange the labels correctly. How to do it?
3. There are 22 blue socks and 35 black socks in your closet.
You need to take a pair of socks from the closet in complete darkness. How many socks do you need to take to be sure you get a matching pair?
4. It takes 30 seconds for an old clock to strike 6 o'clock. How many seconds does it take for the clock to strike 12 o'clock?
5. One lily leaf grows in the pond. Every day the number of leaves doubles. On what day will the pond be half covered with lily leaves if it is known that it will be completely covered with them in 100 days?
6. A passenger elevator rises to the fifth floor at twice the speed of a freight elevator that goes to the third floor.
Which of these two elevators will arrive first: freight to the third floor or passenger to the fifth, if they started from the first floor at the same time?
7. A goose is flying. Towards him is a flock of geese. "Hello, 100 geese," he tells them. They answer: “We are not 100 geese; Now, if there were as many of us as there are now, and even as many, and even half as many and a quarter as many, and even you, then there would be 100 of us geese.
How many geese fly in a flock?
8. Let us prove that 3 = 7. It is known that if the same operation is performed on each part of the equality, then the equality will remain unchanged. Let's subtract five from each part of our equality: 3 - 5 \u003d 7 - 5. It turns out: - 2 \u003d 2. Now let's square each part of the equality: (- 2) 2 \u003d 2 2. It turns out: 4 = 4, therefore: 3 = 7. Find an error in this reasoning.
9. As you know, in any atom there is a nucleus, the dimensions of which smaller sizes the atom itself. If the size of the atomic nucleus is 10–12 cm, and the size of the entire atom is 10–6 cm, then the nucleus is 2 times smaller than the atom itself: 12: 6 = 2. Is this statement true?
If not, how many times atomic nucleus less than an atom?
10. Is it possible to fly to the moon by plane? It must be taken into account that the aircraft are equipped with jet engines, like space rockets, and operate on the same fuel as they do.
11. Is it possible to pierce a fifty-kopeck coin with a needle?
12. A standard glass (200 g) is filled to the brim with water. How many pins can be thrown into it so that not a drop of water spills out of the glass?
13. Ivanov has a portrait hanging in his office. Ivanov is asked: “Who is depicted in this portrait?” Ivanov confusedly answers:
"The father of the person depicted in the portrait is the only son of the father of the speaker." Who is in the portrait?
14. The missionary was captured by the savages, who put him in prison and said: “From here there are only two ways out - one to freedom, the other to death; two warriors will help you get out - one always tells the truth, the other always lies, but it is not known which of them is a liar and which is a truth lover; you can ask any of them only one question.” What question should be asked to get out to freedom?
15. Two ropes of rare silk hang in the monastery. They are attached to the middle of the ceiling at a distance of one meter from each other and reach the floor. The acrobat thief wants to steal as much rope as possible. The height of the ceiling is 20 m. The thief knows that if he jumps or falls from a height of more than 5 m, he will not be able to get out of the monastery. Since he does not have a ladder, he can only climb the rope. He found a way to steal both ropes almost entirely. How to do it?
16. The girl was riding in a taxi. On the way, she talked so much that the driver got nervous. He told her that he was very sorry, but he couldn't hear a word - because his hearing aid didn't work, he was deaf as a cork. The girl fell silent, but when they reached the place, she realized that the driver had played a joke on her. How did she guess?
17. You are in the cabin of an ocean liner at anchor. At midnight, the water was 4 m below the porthole and rose 0.5 m/h. If this speed doubles every hour, how long will it take the water to reach the porthole?
18. Three travelers lay down to rest in the shade of trees and fell asleep. While they slept, the pranksters smeared charcoal on their foreheads. Waking up and looking at each other, they began to laugh, and it seemed to each of them that the other two were laughing at each other.
Suddenly one of them stopped laughing as he realized that his own forehead was also dirty. How did he guess about it?
19. By moving only one of the four matches, make a square (Fig. 45). Matches cannot be bent or broken:
20. As the sun rose, the traveler began to climb the narrow, winding path to the top of the mountain. He walked faster and slower, stopping often to rest. Having done a long way He reached the summit just before sunset. After spending the night at the top, at sunrise he set off on his return journey along the same path. He also descended at an uneven speed, repeatedly resting along the way, and by sunset he reached the foot of the mountain. It is clear that the average rate of descent exceeded the average rate of ascent. Is there such a point on the path that the traveler passed at the same time of day both during the ascent and during the descent?
21. The sculptor has 10 identical statues. He wants three statues on each of the four walls of the hall. How to place them?
22. Draw without lifting the pencil from the paper, following figures(Fig. 46):
23. One mathematician suggested such a deal to a merchant. The mathematician gives the merchant 100 rubles, and the merchant gives the math in exchange for 1 k.
Every next day, the mathematician gives the merchant 100 rubles. more than on the previous one, that is, on the second day he gives him 200 rubles, on the third - 300 rubles. and so on. And the merchant gives the math in return twice as much money as on the previous day, i.e. on the second day he gives him 2 k., on the third - 4 k., on the fourth - 8 k., on fifth - 16 k., etc.
They agreed to make such an exchange within 30 days. Who benefits from this exchange and why?
24. According to the old style, the anniversary of the October Revolution falls on October 25, and according to the new style - on November 7. Thus, all events according to the old style precede the same events according to the new style by 13 days. So, if according to the new style New Year falls on January 1, then according to the old style it should fall on December 19. Why then do we celebrate the old New Year on January 14?
25. A drawing of a glass filled with wine was made from matches (Fig. 47). Rearrange two matches so that in the newly received picture the wine is outside the glass. When demonstrating the role of wine, a match can play:
26. How to arrange six cigarettes in such a way that they are all in contact with each other, that is, that each of them touches the other five?
27. Three people are standing in front of you. One of them is a Truth-lover (always tells the truth), another is a Liar (always lies), and the third is a Diplomat (sometimes tells the truth, sometimes lies). You do not know who is who and ask a question to the person who is standing on the left:
- Who is standing next to you?
“Truth,” he replies.
Then you ask the person in the center:
- Who are you?
“Diplomat,” he replies.
And finally, you ask the person on the right:
- Who is standing next to you?
“Liar,” he replies.
Who is on the left, who is on the right, who is in the center?
28. There are 10 liters of wine in a ten-liter bucket. You have two empty buckets at your disposal: one - 7 liters, and the other - 3 liters. How to use these buckets to divide 10 liters of wine into two identical parts of 5 liters by transfusions?
29. Andrei's watch is 10 minutes behind, but he is sure that they are 5 minutes ahead. He agreed with Katya to meet at 8:00 at the train to go out of town. Katya's watch is 5 minutes fast, but she thinks it is 10 minutes behind. Which one will be the first to get on the train?
30. A 110-year-old turtle asked a dinosaur, "How old are you?" The dinosaur, accustomed to expressing himself in a complex and confusing way, replied: “I am now 10 times older than you were when I was the same age as you are now.” How old is the dinosaur?
31. The car thief stole a car while trying to get into the checkpoint B, however, was discovered by the police at the checkpoint A. Leaving the chase, he began to dodge, moving from A in B along the curve ACDB along the arcs of small semicircles as shown by the arrows (Fig. 48). The policemen chasing him started from A a moment later and, hoping to intercept the hijacker at the point B, set off along the arc of a great semicircle. Will they catch up with the hijacker at the point B, if their speeds are exactly the same (Fig. 48)?
32. Katya is twice as old as Nastya will be when Olya is as old as Katya is now. Who is the oldest and who is the youngest?
33. In one class, the students were divided into two groups. Some had to always tell only the truth, while others - only a lie. All students of the class wrote an essay on a free topic, and at the end of the essay, each student had to attribute one of the phrases: “Everything written here is true”, “Everything written here is a lie”. In total, there were 17 truth-tellers and 18 liars in the class. How many essays with a statement about the veracity of what was written did the teacher count when checking the work?
34. How many great-great-grandparents did all your great-great-grandparents have in total?
35. A handkerchief lies unfolded on the table. On it in the center is an empty neck down Glass bottle. How to pull a handkerchief out from under a bottle without touching it?
36. On the left side of the equality, you need to put only one dash (stick) in order for the equality to turn out to be true:
5 + 5 + 5 = 550.
37. Let us prove that three times two will not be six, but four.
Take a match, break it in half. It's one time two. Then take a half and break it in half. This is the second time twice. Then take the remaining half and break it in half too. This is the third time twice. It turned out four. Therefore, three times two is four, not six. Find the error in this reasoning.
38. How to connect nine dots to each other with four lines without lifting the pencil from the paper (Fig. 49)?
In a hardware store, a customer asked:
- How much does one cost?
“Twenty roubles,” answered the seller.
How much is twelve?
- Forty rubles.
- Okay, give me a hundred and twelve.
- Please, sixty rubles from you.
What did the visitor buy?
40. If it rains at 12 o'clock at night, can we expect that in 72 hours there will be sunny weather?
41. Three people paid 30 rubles for lunch. (each for 10 rubles). After they left, the hostess discovered that dinner cost not 30 rubles, but 25 rubles. and sent the boy in pursuit to return 5 p. Each of the travelers took 1 r., and 2 r. they left the boy. It turns out that each of them paid not 10 rubles, but 9 rubles. There were three of them: 9 3 = 27, and the boy had two more rubles: 27 + 2 = 29. Where did the ruble go?
42. 1,000,000 liters of water were poured into a pool of 1 ha. Can you swim in this pool?
43. Which is more: or?
44. One boy does not have enough to the cost of the ruler 24 k., and the other does not have enough to this cost 2 k. When they put their money together, they still could not buy the ruler. How much does a line cost?
45. In one parliament, the deputies were divided into conservatives and liberals. The conservatives spoke only the truth on even numbers, and only untruths on odd numbers. Liberals, on the other hand, told only the truth on odd numbers, and only lies on even numbers. How, with the help of one question posed to any deputy, it is possible to determine exactly what date today is: even or odd? Answers should be definite: "yes" or "no".
46. A bottle with a cork costs 1 p. 10 k. A bottle is more expensive than a cork by 1 p. How much is the bottle and how much is the cork?
47. Katya lives on the fourth floor, and Olya lives on the second. Rising to the fourth floor, Katya overcomes 60 steps. How many steps does Olya need to climb to get to the second floor?
48. A mathematician wrote a two-digit number on a piece of paper. When he turned the paper upside down, the number decreased by 75. What number was written?
49. A rectangular sheet of paper is folded in half 6 times. On a folded sheet, not on the folds, 2 holes were made. How many holes will there be on the sheet if it is unfolded?
50. Two fathers and two sons caught three hares: one each.
How is this possible?
51. The interlocutor invites you to think of any three-digit number. Then he asks to duplicate it to get a six-digit number. For example, you thought of the number 389, duplicating it, you get a six-digit number - 389,389; or 546 - 546 546, etc.
Further, the interlocutor offers you to divide this six-digit number by 13. “Suddenly it will turn out without a trace,” he says. You divide with a calculator (you can do it without it) and indeed your number is divisible by 13 without a remainder. Then he offers you to divide the result by 11. You divide, and again it turns out without a remainder. And finally, the interlocutor asks you to divide the resulting result by 7. The division not only goes without a remainder, but also results in the same three-digit number that you arbitrarily chose first. How does this happen?
52. Divide the figure, consisting of three identical squares, into four equal parts (Fig. 50):
53. One hundred schoolchildren simultaneously studied English and German languages. At the end of the course, they took an exam, which showed that 10 students did not master either one or the other language. Of the remaining German students, 75 passed, and 83 passed the English exam. How many test takers speak both languages?
54. How to pour exactly half from a mug, ladle, pan and any other dishes of the correct cylindrical shape, filled to the brim with water, without using any measuring instruments?
55. Hour and minute hands sometimes coincide, for example at 12 o'clock or at 24 o'clock. How many times will they coincide between 6 o'clock in the morning of one day and 10 o'clock in the evening of another day?
56. The ship sails from Nizhny Novgorod to Astrakhan in 5 days, it makes the return journey at the same speed in 7 days. How many days does it take a raft to sail from Nizhny Novgorod to Astrakhan?
57. Three hens lay three eggs in three days. How many eggs will 12 hens lay in 12 days?
58. How to write the number 100 using five units and action signs?
59. Let's calculate how many days a year we work and how many we rest. There are 365 days in a year. Everyone sleeps eight hours a day, that's 122 days a year. Subtract, 243 days remain. Eight hours a day is spent resting after work, which is also 122 days a year. Subtract, there are 121 days left. On weekends, which are 52 a year, no one works. Subtract, there are 69 days left. Further, a four-week vacation is 28 days. Subtract, there are 41 days left. Approximately 11 days a year are occupied by various holidays. Subtract, there are 30 days left. Thus, we work only one month a year.
60. In one row are three glasses filled with water and three empty (Fig. 51). How to make it so that filled and empty glasses alternate if you can only take one glass in your hands?
61. If 1 worker can build a house in 12 days, then 12 workers will build it in 1 day. Therefore, 288 workers will build a house in 1 hour, 17,280 workers will build it in 1 minute, and 1,036,800 workers will be able to build a house in 1 second. Is this reasoning correct? If not, what is the error?
62. What word is always spelled wrong? (The task is a joke.)
63. "I vouch," said the salesman at the pet store, "that this parrot will repeat every word it hears." A delighted buyer bought a miracle bird, but when he came home, he found that the parrot was as mute as a fish. However, the seller did not lie. How is this possible? (The task is a joke.)
64. There is a candle and a kerosene lamp in the room. What will you light first when you enter this room in the evening?
65. Peter was very tired and went to bed at 7 o'clock in the evening, setting a mechanical alarm clock for 9 o'clock in the morning. How many hours will he get to sleep?
66. The negation of a true sentence is a false sentence, and the negation of a false one is true. However, the following example says that this is not always the case. The sentence "This sentence contains six words" is false because it has five words instead of six. But the negation: “This sentence does not contain six words,” is also false, since it has just six words. How to resolve this misunderstanding?
67. How many eight-digit numbers are there whose sum of digits is two?
68. The perimeter of a figure made up of squares is six (Fig. 52). What is its area?
69. What is the difference between the cube of the sum of the squares of the numbers 2 and 3 and the square of the sum of their cubes?
70. Half of half a number is equal to half. What is this number?
71. Over time, a person will definitely visit Mars. Sasha Ivanov is a man. Consequently, Sasha Ivanov will eventually visit Mars. Is this reasoning correct? If not, what is wrong with it?
72. To get orange paint, mix 6 parts yellow paint with 2 parts red. There are 3 g of yellow paint and 3 g of red.
How many grams of orange paint can be obtained in this case?
73. 4 squares are made out of 12 matches (Fig. 53). How should 2 matches be removed so that 2 squares remain?
74. What sign should be placed between the numbers 5 and 6 so that the resulting number is greater than 5 but less than 6?
75. In football team 11 players. Them average age is equal to 22 years. During the match, one of the players was eliminated. At the same time, the average age of the team became equal to 21 years. How old is the eliminated player?
76. – How old is your father? the boy is asked.
“As much as I do,” he replies calmly.
- How is this possible?
- Very simple: my father became my father only when I was born, because before my birth he was not my father, so my father is the same age as me.
Is this reasoning correct? If not, what is wrong with it?
77. There are 24 kg of nails in a bag. How can you measure 9 kg of nails on a pan balance without weights?
78. Peter lied from Monday to Wednesday and told the truth on other days, and Ivan lied from Thursday to Saturday and told the truth on other days. One day they said in the same way: "Yesterday was one of the days when I lie." What day was yesterday?
79. A three-digit number was written in numbers, and then in words. It turned out that all the numbers in this number are different and increase from left to right, and all words begin with the same letter. What is this number?
80. An error was made in the equality made up of matches: How should one match be shifted in order for the equality to become true?
81. How many times will a three-digit number increase if the same number is added to it?
82. If there were no time, there would not be a single day. If there were no day, it would always be night. But if it were always night, there would be time. Therefore, if there were no time, there would be. What is the reason for this misunderstanding?
83. Each of two baskets contains 12 apples. Nastya took a few apples from the first basket, and Masha took from the second as many as were left in the first. How many apples are left in the two baskets together?
84. One farmer has 8 pigs: 3 pink, 4 brown and 1 black.
How many pigs can say that in this small herd there is at least one more pig of the same color as her own? (The task is a joke.)
85. The only son of a shoemaker's father is a carpenter. Who is the cobbler to the carpenter?
86. If 1 worker can build a house in 5 days, then 5 workers will build it in 1 day. Therefore, if 1 ship crosses the Atlantic Ocean in 5 days, then 5 ships will cross it in 1 day. Is this statement correct? If not, what is the error in it?
87. Returning from school, Petya and Sasha went to the store, where they saw big scales.
“Let's weigh our portfolios,” suggested Petya.
The scales showed that Petya's portfolio weighed 2 kg, while Sasha's portfolio weighed 3 kg. When the boys weighed the two briefcases together, the scales showed 6 kg.
- How so? Petya was surprised. Because 2 plus 3 does not equal 6.
- Can't you see? Sasha answered him. - The arrow has shifted on the scales.
What is the real weight of portfolios?
88. How to place 6 circles on the plane in such a way that you get 3 rows of 3 circles in each row?
89. After seven washes, the length, width and height of a bar of soap has halved. How many washes will the remaining piece last?
90. How to cut off 1/2 m from a piece of matter 2/3 m without the help of any measuring instruments?
91. It is often said that one must be born a composer, or an artist, or a writer, or a scientist. Is this true? Is it really necessary to be born as a composer (artist, writer, scientist)?
(The task is a joke.)
92. In order to see, it is not at all necessary to have eyes.
We see without the right eye. We also see without the left. And since we have no other eyes besides the left and right eyes, it turns out that neither eye is necessary for vision. Is this statement true? If not, what is wrong with it?
93. The parrot lived less than 100 years and can only answer yes and no questions. How many questions does he need to ask to find out his age?
94. Say how many cubes are shown in Figure 54:
95. Three calves - how many legs? (The task is a joke.)
96. One man who fell into captivity tells the following: “My dungeon was in the upper part of the castle. After many days of effort, I managed to break one of the bars in narrow window. It was possible to crawl through the resulting hole, but the distance to the ground was too great to simply jump down. In the corner of the dungeon, I found a rope forgotten by someone. However, it turned out to be too short to be able to go down it. Then I remembered how one wise man lengthened a blanket that was too short for him, cutting off part of it from below and sewing it on top. So I hurried to split the rope in half and re-tie the two resulting parts. Then it became long enough, and I safely went down it. How did the narrator manage to do this?
97. The interlocutor asks you to think of any three-digit number, and then offers to write down its numbers in reverse order to get another three-digit number. For example, 528 - 825, 439 - 934, etc. Then he asks to subtract the smaller number from the larger number and tell him the last digit of the difference. After that, he names the difference. How he does it?
98. Seven walked - they found seven rubles. If not for seven, but for three, would you find a lot? (The task is a joke.)
99. Divide the drawing, consisting of seven circles, with three straight lines into seven parts so that each part contains one circle:
100. The globe was pulled together by a hoop along the equator. Then the length of the hoop was increased by 10 m. At the same time, a small gap formed between the surface of the globe and the hoop. Can a person get through this gap? The length of the earth's equator is approximately 40,000 km.
Description of the presentation on individual slides:
1 slide
Description of the slide:
Baal Island is inhabited only by humans and strange monkeys that cannot be distinguished from humans. Any of the inhabitants of the island speaks either only the truth, or only a lie. Who are the next two? A: “B lying monkey. I am human." B: "A told the truth." Task #1
2 slide
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SOLUTION: The double statement used by A is true only if both parts of it are true. Let's assume B- fair man, then A is also honest (which is what B says), so B is a knave, as A claims, which contradicts our assumption. Therefore B is a knave. Knowing this very well, B said that A was also a liar. Thus, A's first statement is a lie, and B is not a lying monkey. However, B, as we have already found out, is definitely a liar, which means that B is not a monkey. B is a dishonest person. The second statement A shows us that A is a monkey. Therefore, A is a lying monkey.
3 slide
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Task №2 Three goddesses sat in an ancient Indian temple: Truth, Falsehood and Wisdom. Truth only tells the truth, Falsehood always lies, and Wisdom can tell the truth or lie. The pilgrim asked the goddess on the left: “Who is sitting next to you?” "True," she replied. Then he asked the middle one: “Who are you?” "Wisdom," she replied. Finally he asked the one on the right, “Who is your neighbor?” "False," replied the goddess. And after that, the pilgrim knew exactly who was who.
4 slide
Description of the slide:
Solution: Let's designate each goddess with a certain letter. We have the following statements at our disposal: 1. A says that B is True. 2. B says she is Wisdom. 3. C says that B is False. The first sentence tells us that A is not True. The second sentence was also not told by the Truth, therefore the Truth is C. Whence it is clear that the last sentence is true: B is False, and A is Wisdom.
5 slide
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Task number 3 There are three coins on the table: gold, silver and copper. If you say a statement that turns out to be true, you will be given a coin. Nothing will be given to you for lying. What do you have to say to get a gold coin?
6 slide
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Solution: "You will give me neither a copper nor a silver coin." If this statement is true, then they will give me a gold coin. If my statement is false, then the reverse statement must be true, namely: "You will give me either a copper or a silver coin." But then this contradicts the conditions of the task - they should not give coins for a lie. Therefore, the original statement is true.
7 slide
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Task number 4 You arrived at a fork in the two roads. One of them leads to the False City, where there is a general store for the clues of the Universe, which are released for free. Another road leads to Pravdograd, where there is a gas station. Residents of False City always lie, and residents of Pravdograd always tell the truth and nothing but the truth. At the fork, one representative from each of the two cities is on duty. You don't know which one is from where. How to find out which road leads to Pravdograd if you are allowed to ask only one question to only one representative?
8 slide
Description of the slide:
Solution: There are several options for such questions. Indirect question: “Hey you! What will that person say if I ask him where this road leads? The answer to such a question will always contradict where the road actually leads. Trick question: “Hey you! That person who is on duty at the road leading to Pravdograd, is he from there? The answer will be positive only in two cases: either this is a resident of Pravdograd, standing on the road to Pravdograd, or a resident of False City, standing on the same road. In both cases, you can be sure that with an affirmative answer, this road will really lead you to Pravdograd. In the same way, a negative question can be formulated. Or another tricky question: “Hey you! What would you say if I asked you...?”. A resident of Pravdograd will always answer the truth, and a resident of Lzhegrad will lie. However, due to the wording of the question, the liar will have to lie twice, that is, to tell the truth.
9 slide
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Task №5 Peter lied from Monday to Wednesday and told the truth on other days, and Ivan lied from Thursday to Saturday and told the truth on other days. One day they said in the same way: "Yesterday was one of the days when I lie." What day did they say this?
10 slide
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Solution: It was Thursday. On this day, Peter truthfully said that yesterday (i.e. on Wednesday) he lied, and Ivan lied about the fact that yesterday (i.e. on Wednesday) he lied, because according to the condition on Wednesday he was telling the truth.
11 slide
Description of the slide:
Task number 6 Lady Cat said: “I am the most beautiful. Mary is not the most beautiful." Jane said, “Kat is not the prettiest. I am the most beautiful." And Mary just said, "I'm the most beautiful." The white knight suggested that all the statements of the most beautiful of the girls are true, and all the statements of the other ladies are false. Based on this, determine the most beautiful of the ladies.
123. What sign must be placed between the numbers 5 and 6 so that the resulting number is greater than 5 but less than 6?
5 < 5? 6 < 6
124. There are 11 players on a football team. Their average age is 22 years. During the match, one of the players dropped out. At the same time, the average age of the team became equal to 21 years. How old is the eliminated player?
125 – How old is your father? the boy is asked.
“As much as I do,” he replies calmly.
- How is this possible?
- Very simple: my father became my father only when I was born, because before my birth he was not my father, then my father is the same age as me.
Is this reasoning correct? If not, what is wrong with it?
126. There are 24 kg of nails in a bag. How can you measure 9 kg of nails on a pan balance without weights?
127. Peter lied from Monday to Wednesday and told the truth on other days, and Ivan lied from Thursday to Saturday and told the truth on other days. One day they said in the same way: "Yesterday was one of the days when I lie." What day was yesterday?
128. A three-digit number was written in numbers, and then in words. It turned out that all the numbers in this number are different and increase from left to right, and all words begin with the same letter. What is this number?
129. A mistake was made in the equality made up of matches. How should one match be shifted in order for the equality to become true?
130. How many times will a three-digit number increase if the same number is added to it?
131. If there were no time, there would not be a single day. If there were no day, it would always be night. But if it were always night, there would be time. Therefore, if there were no time, there would be. What is the reason for this misunderstanding?
132. There are 12 apples in each of two baskets. Nastya took a few apples from the first basket, and Masha took from the second as many as were left in the first. How many apples are left in the two baskets together?
133. One farmer has eight pigs: three pink, four brown and one black. How many pigs can say that in this small herd there is at least one more pig of the same color as her own? (The task is a joke).
134. There are two identical buckets filled with water on two scales. The water level in them is the same. Floats in one bucket wooden block. Will the scales be in balance?
135. If one worker can build a house in 5 days, then 5 workers will build it in one day. Therefore, if one ship crosses the Atlantic Ocean in 5 days, then 5 ships will cross it in one day. Is this statement true? If not, what is the error in it?
136. Returning from school, Petya and Sasha went to the store, where they saw a large scale.
“Let's weigh our portfolios,” suggested Petya.
The scales showed that Petya's portfolio weighed 2 kg, while Sasha's portfolio weighed 3 kg. When the boys weighed the two briefcases together, the scales showed 6 kg.
“How is it,” Petya was surprised, “because 2 + 3 is not equal to 6.
- Can't you see? - Sasha answered him, - the scale has shifted the arrow.
What is the real weight of portfolios?
137. How to place six circles on a plane in such a way that there are three rows of three circles in each row?
138. After seven washes, the length, width and height of a bar of soap has halved. How many washes will the remaining piece last?
139. How to cut off half a meter from a piece of matter 2/3 m without the help of any measuring instruments?
140. 13 identical sticks are drawn on a rectangular sheet of paper at an equal distance from each other (see figure). The rectangle is cut along the straight line AB passing through the upper end of the first stick and through the lower end of the last. After that, both halves are shifted as shown in the figure. Surprisingly, instead of 13 sticks there will be 12. Where and how did one stick disappear?
141. It is often said that one must be born a composer, or an artist, or a writer, or a scientist. Is this true? Is it really necessary to be born as a composer (artist, writer, scientist)? (The task is a joke).
142. In order to see, it is not at all necessary to have eyes. We see without the right eye. We also see without the left. And since we have no other eyes besides the left and right eyes, it turns out that neither eye is necessary for vision. Is this statement true? If not, what is wrong with it?
143. A parrot has lived less than 100 years and can only answer yes and no questions. How many questions does he need to ask to find out his age?
144. How many cubes are shown in this picture?
145. Three calves - how many legs? (The task is a joke).
146. One person who fell into captivity tells the following. "My dungeon was in the upper part of the castle. After many days of effort, I managed to break one of the bars in a narrow window. It was possible to climb through the resulting hole, but the distance to the ground left no hope of just jumping down. rope. However, it turned out to be too short to climb down. Then I remembered how a wise man lengthened a blanket too short for him, cutting off part of it from below and sewing it on top. So I hastened to divide the rope in half and again tie the two resulting parts Then it became long enough, and I safely went down it." How did the narrator manage to do this?
147. The interlocutor asks you to think of any three-digit number, and then offers to write down its numbers in reverse order to get another three-digit number. For example, 528–825, 439–934, etc. Then he asks to subtract the smaller number from the larger number and tell him the last digit of the difference. After that, he names the difference. How he does it?
148. Seven walked - they found seven rubles. If not for seven, but for three, would you find a lot? (The task is a joke).
149. How to divide a drawing consisting of seven circles by three straight lines into seven parts in such a way that each part contains one circle?
150. The globe was pulled together by a hoop along the equator. Then the length of the hoop was increased by 10 m. At the same time, a small gap formed between the surface of the globe and the hoop.
Can a person get through this gap? (The length of the earth's equator is approximately 40,000 km).
151. A tailor has a piece of cloth 16 meters long, from which he cuts 2 meters daily. After how many days will he cut the last piece?
152. Four equal squares are built from 12 matches. How to shift three matches in such a way that you get three equal squares?
153. A wheel with blades is installed near the bottom of the river, and it can rotate freely. If the river flows from left to right, in which direction will the wheel turn? (See picture).
DID EISENHAUER LIE?
This episode, narrated by prominent US military and politician Dwyde Eisenhower, last years often quoted. Yes, in his documentary about the Great Patriotic War, he was beaten by the popular television master Yevgeny Kiselev. In his largely controversial book, "Unknown Zhukov: a portrait without retouching", he is cited as an example by the writer Boris Sokolov (By the way, in 2001, in one of the central newspapers, I had to read in an article dedicated to Marshal Zhukov about the same episode, but without reference to the original source, as a matter of course. Say, the marshal was controversial, although he was talented. But on the mined fields, before launching equipment on them, he drove infantry forward, etc. see above.). Here is this passage: “I was very struck by the Russian method of overcoming minefields, which Zhukov told about,” Eisenhower wrote in his book Crusade to Europe. “German minefields, covered by fire, were a serious tactical obstacle and caused significant losses and delay It was difficult to break through them, although our specialists used various mechanical devices to safely undermine them.Marshal Zhukov told me about his practice, which, roughly speaking, boiled down to the following: "When we approach a minefield, our infantry conducts attack as if the minefield does not exist. The losses suffered by troops from anti-personnel mines are considered to be only equal to those that we would suffer from artillery and machine-gun fire if the Germans covered the area not only with minefields, but with a significant number of troops. Attacking infantry does not detonate anti-tank mines. When it reaches the far end of the field, a passage is formed through which sappers go and remove anti-tank mines so that the equipment can be launched. "I vividly imagined what would happen if any American or British commander adopted such tactics, and more vividly imagined what people in any of our divisions would say if they tried to make the practice of this kind part of their military doctrine.
These words of a major military leader of the Second World War, and later one of the presidents of the United States of America, of course, would be impossible to read without horror if they corresponded to the truth. But let's try to figure out whether the above is true without unnecessary emotions.
In the film directed by Yevgeny Matveev "Fate" there is an episode: SS men under the barrels of machine guns force our captured soldiers to drag harrows through a minefield. In this case, the Nazis, or the authors of the film, understood that simply to drive the prisoners without technical means, i.e., harrows, there will be few effective occupation- part of the mines will definitely be missed and remain in the same combat state. Consequently, a simple attack to clear the fields (if you still imagine that such a thing took place) would be even less effective. After all, people are not robots - they would definitely start looking for loopholes (a wider jump, running along already laid tracks in front of the runner). This would nullify all the "strategic" plans of the commanders.
In conversations with veterans of the Great Patriotic War, I had to make sure more than once that none of them, who came out alive from the bloodiest battles, who lost hundreds and thousands of their comrades, had never heard of anything like that. But, apparently, we are talking about the massive use of such a strategy. Therefore, witnesses should have remained (at least one of those who ran to the edge of the field!). By the way, none of those who quoted the American marshal cited any other evidence as an example (In Sokolov's book, however, there is an excerpt from a letter from a German soldier, but it is written very indistinctly and is not very convincing). Also distrustfully reacted to the bike, told by the famous American marshal, as a matter completely meaningless from a technical point of view, and explosives experts with whom I had to talk.
Another thing is also curious, Georgy Konstantinovich, allegedly talking about the advantages of this "most better way overcoming minefields", meant the military operations of the Red Army in Europe. That is, those operations when the country had already overcome the crisis of lack modern weapons when the Red Army learned to use these weapons and when, finally, this army became especially in need of human resources. This is evidenced even by the fact that by the year 44, 17-year-old boys began to be drafted into the army, who died in the very first battles. And then, thanks to the victories in Europe, many of those 17-year-olds who survived were recalled back to the rear in order to protect them from further extermination. That is, about endless human resources Soviet Union needless to say - this is another myth invented in the West. (It must also be borne in mind that the Second World War was a war between two economies and significant human resources had to be kept in the rear in production.)
Meanwhile, from the time when the Red Army stopped retreating, barrage detachments ceased to be used (which, by the way, in various versions and in different time, existed in other armies of the world), and no one even urged penal companies to attack with fire in the back.
Of course, Americans are forgiven for imagining Soviet soldiers so deprived own will zombies, capable of good will, lining up in close ranks and typing a step (only in this way, if you obey logic, you can be guaranteed to clear the minefield from explosive devices), under enemy fire, follow the order of your immediate commander, who immediately, in accordance with the charter, must step forward. To imagine this, I repeat, is forgivable for Americans (in modern Hollywood films you can see thousands of absurdities about our past and present), but perhaps we, Russians, should not take on faith any heresy that is published today in various dubious publications?
However, the question arises: how, in this case, did the infantry pass through minefields during attacks? The answer to it is given by the American military themselves, veterans of the Second World War. During the landing operation on the coast of Normandy, which marked the opening of the Second Front, which was directly commanded by Eisenhower, the Allies just encountered the very minefields and wire fences that one of the best top commanders of the German army of that time, Erwin Rommel, took care of with German pedantry . To the credit of the allies, these barriers could not become a serious obstacle to the landing. They acted with minefields ingeniously and simply (the technology, by the way, was worked out back in the First World War) - corridors were made in them with the help of aerial bombs and heavy artillery. By the way, mines are destroyed by detonation even today - the Americans used super-heavy bombs to destroy mines during the famous "Desert Storm" in 1991, and even in 2004 during the occupation of Iraq. And by 1944, the Red Army had an advantage over the German in artillery by about 20:1. And Zhukov, if only to save one time and money, would certainly have preferred in this case artillery shelling in squares to the masses of infantry, whose numerical advantage over the German one was not so overwhelming.
So, a professional military man would never take on faith the words of the Soviet Marshal, if they were actually uttered. Why, then, was Eisenhower cunning in his book? Perhaps the American was simply jealous of the success of his Russian colleague and was looking for a reason to justify himself to his fellow citizens for the much smaller achievements of the armies he led. In addition, Eisenhower already at that time saw himself as a future politician (as he himself testifies in his book) and, naturally, sought to gain popularity among voters as a politician. And what is the meaning of the word spoken by a politician who wants to be elected - the Russians have already had the opportunity to make sure more than once. So Eisenhower bought his electorate cheaply with this "Russian horror story." Say, we, the Americans, lagged behind the pace of the advance of the Soviet troops in the Second World War because the minefields were cleared with the help of technology. And if they did it like Russians (that's the secret of success!), then not only in Berlin, they would have been in Moscow long ago!
But perhaps this is not the whole truth. The most interesting thing is that G.K. Zhukov could really tell this "terrible story" to Eisenhower. He, in turn, could "buy" a naive American (after all, it is known that guests from overseas often do not catch our domestic humor). And judging by the notes of eyewitnesses, Georgy Konstantinovich was a master at such jokes, apparently hiding his irritation behind them at times. When, under Khrushchev, he was massacred at one of the meetings of the Politburo, accusing him of Bonapartism, he answered not without a challenge: "Bonaparte lost the war, but I won!" When one of the Soviet newspapers already in the post-war years asked a number of military marshals, is it possible to get this highest military rank in peacetime? He alone answered in the affirmative that yes, if you study a lot and, among other things, pay more attention to Marxism (they say that at that time they were already trying to assign the marshal rank to Khrushchev). What is this if not a hidden mockery? And, to the generally idle question of an American, when any operation, including those carried out by the Red Army in order to divert forces from the front in the West, cost hundreds of thousands of lives, you see, the evil irony was quite appropriate.
So, perhaps, from a misunderstood joke, an unsubstantiated statement was born, which suddenly pops up in one or another publication dedicated to our outstanding commander. Having broken the back of the best army in the world, which until the age of 43 was German Army, The Red Army, at that time, undoubtedly acquired the qualities of the best itself. The Americans and the British did not have such rich experience in combat operations in the field. Our military equipment (especially ground-based) surpassed all foreign analogues in many respects. After the Battle of Kursk-Oryol, Soviet generals fought with fewer losses than their opponents.
Of course, the losses, especially in the initial period of the war, were enormous. They were there later - probably, the youth and poor training of so many of our commanders and privates affected. But even that war was incredibly cruel. It was a war not of armies, but of countries and peoples. In its second period, starting with Stalingrad, the Germans also suffered completely senseless and unjustified losses. The Americans and the British, fighting on foreign territory, were unaware of such fury, where they spare neither themselves nor the enemy. From today's standpoint it is not possible to give a completely objective assessment of those events. And before condemning the past, let's look back at ourselves today. Is it not these days that conscript boys were sent to die in Chechnya? Let's look back and see how indifferent we are to our compatriots today.
