Svetlana Tyulyakova
Didactic games from the Entertaining Logic club
Didactic games from the Entertaining Logic club
The reason for writing this post was my thinking that the site contains a lot of material that is difficult to find due to the age. and Azhar Tukzhanova's comment to my post in which she wrote the following:
Svetlana, I am very glad to meet you. You are a wonderful and creative person. There are always so many interesting things in your blog. You supported me at the very beginning, when it was very difficult for me to navigate the site. Indeed, beginners always need help and you provide it, despite being busy. You have created the much needed "Methodical Work" club. And the fact that you have facilitated the search for beginners on the site, for example, in the search for didactic games - "Didactic and other games in colleagues' blogs" already with links.
Svetlana, thank you for your attention and information, your materials are always timely and very necessary (I think that many colleagues will support me).
So today I went to one of these clubs, which is currently almost not functioning, and found there a little of such information. I decided to pull it out for all users. By writing a generic post with links to games. I don't know if the moderators will miss it, but I'll try.
In the blog of MARIA CHERENKOVA and her club "Entertaining Logic" you will find wonderful didactic games.
I hope Maria will not be offended by my placement, as I believe that this will attract more users to her club and give it a higher rating for her club.
THE GAME "BURNS - DOES NOT BURN", "SINKS - DOES NOT Sink"
Didactic games "Reason".
Didactic game "Choose what fits" to the lesson on coherent speech "Three woodcutters"
Didactic game "What will burn and what will not?"
Didactic game "Heavy - light"
Didactic game "Match a couple"
Games for training logical thinking.
Didactic game "Cold - hot"
Tasks for preschoolers to develop logical thinking.
***
FGT in the work of the circle. Planning of work on the topic “Knowledge Day. School"
FGT in the work of the circle. Complex thematic planning on the topic “Knowledge Day. School"
Materials of work D / I "The fourth extra"
Materials of work D / I "Complete the offer"
Materials of work D / I "Pick a pair"
***
Complex thematic planning on the topic “Vegetables. Garden"
Planning work on the topic “Vegetables. Garden"
Materials of work: cards for the game "Agree a phrase" on the topic "Vegetables. Garden"
Materials of work: cards for the game "Lay out correctly" on the topic "Vegetables. Garden"
Work materials: cards for the game "Choose the right vegetable" on the topic "Vegetables. Garden"
***
Complex thematic planning on the topic “Fruits. Garden"
Planning work on the topic “Fruits. Garden"
Materials of work: cards for the game "Fill in the empty cells" on the topic "Fruits. Garden"
Materials of work: cards for the game "Close only fruits" on the topic "Fruits. Garden"
Materials of work: cards for the game "Compare with each other" on the topic "Fruits. Garden"
1. Explanatory note
1.1 Relevance
1.2 Purpose of the program
1.3 Program objectives
1.4 Terms of implementation of the program, age of children, forms of conducting classes
1.5 Stages of program implementation
1.6 Program content
1.7 Expected results
2. Methodological support
2.1 Prospective-thematic plan of the circle "Entertaining logic"
3. Diagnostic program of logical thinking for older preschool children.
5. Information resources
1. Explanatory note.
Why does a little preschooler need logic?
According to LA Venger, “for five-year-old children, the external properties of things are clearly not enough. They are quite ready to gradually get acquainted not only with external, but also with internal, hidden properties and relationships that underlie scientific knowledge about the world ... All this will benefit the mental development of the child only if the training is aimed at development mental abilities, those abilities in the field of perception, imaginative thinking, imagination, which are based on the assimilation of samples of the external properties of things and their varieties ... "
The skills and abilities acquired by the child in the preschool period will serve as the foundation for acquiring knowledge and developing abilities at an older age - at school. And the most important among these skills is the skill of logical thinking, the ability to "act in the mind." A child who has not mastered the techniques of logical thinking will find it more difficult to solve problems, performing the exercises will require a lot of time and effort. As a result, the child's health may suffer, interest in learning will weaken or completely fade away.
Having mastered logical operations, the child will be more attentive, learn to think clearly and clearly, and will be able to concentrate on the essence of the problem at the right time. It will become easier to study, which means that both the learning process and school life itself will bring joy and satisfaction.
This program shows how, through special games and exercises, you can form the ability of children to independently establish logical relationships in the surrounding reality.
Working with preschoolers on the development of cognitive processes, you come to the conclusion that one of the necessary conditions for their successful development and learning is consistency, i.e. a system of special games and exercises with consistently developing and increasingly complex content, with didactic tasks, game actions and rules. Separately taken games and exercises can be very interesting, but using them outside the system cannot achieve the desired learning and developmental result.
1.1 Relevance
To successfully master the school curriculum, a child needs not only to know a lot, but also to think consistently and conclusively, to guess, to show mental stress, to think logically.
Teaching the development of logical thinking is of no small importance for the future student and is very important today.
Mastering any method of memorization, the child learns to single out a goal and carry out certain work with the material for its implementation. He begins to understand the need to repeat, compare, generalize, group material in order to memorize.
Teaching children to classify contributes to the successful mastering of a more complex way of memorization - a semantic grouping with which children meet at school.
Using the opportunities for the development of logical thinking and memory of preschoolers, it is possible to more successfully prepare children for solving the problems that school education poses for us.
The development of logical thinking includes the use of didactic games, ingenuity, puzzles, solving various logic games and labyrinths and arouses great interest in children. In this activity, important personality traits are formed in children: independence, resourcefulness, ingenuity, perseverance is developed, constructive skills are developed. Children learn to plan their actions, think them over, guess in search of a result, while showing creativity.
Working with children, you can see that many children do not cope with seemingly simple logical tasks. For example, most older preschool children cannot correctly answer the question of which is more: fruits or apples, even if they have a picture in their hands on which fruits are drawn - many apples and a few pears. Children will answer that there are more pears. In such cases, they base their responses on what they see with their own eyes. They are "let down" by figurative thinking, and children by the age of 5 still do not know logical reasoning. In older preschool age, they begin to manifest elements of logical thinking, characteristic of schoolchildren and adults, which need to be developed in identifying the most optimal methods for the development of logical thinking.
Games of logical content help to instill in children a cognitive interest, contribute to research and creative search, the desire and ability to learn. Didactic games as one of the most natural activities of children and contributes to the formation and development of intellectual and creative manifestations, self-expression and independence. The development of logical thinking in children through didactic games is important for the success of subsequent school education, for the correct formation of the student's personality and in further learning will help to successfully master the basics of mathematics and computer science.
1.2 Purpose of the program: creation of conditions for the maximum development of logical thinking of preschoolers in preparation for successful schooling.
1.3 Program objectives:
- teach children basic logical operations: analysis, synthesis, comparison, denial, classification, systematization, limitation, generalization, inferences
- teach children to navigate in space
- develop in children higher mental functions, the ability to reason, prove
- foster the desire to overcome difficulties, self-confidence, the desire to come to the aid of a peer
1.4 Terms of implementation of the program, age of children, forms of conducting classes
Terms of program implementation - 1-2 years
The program is designed for children 5-7 years old
The program provides for conducting circle classes in various forms:
- Individual independent work of children.
- Work in pairs.
- Group forms of work.
- Differentiated.
- Frontal check and control.
- Self-assessment of the work performed.
- Didactic game.
- Competition.
- Contests.
1.5 Stages of program implementation
The technology of activity is built in stages:
- Diagnostics of the initial level of development of cognitive processes and control over their development.
- Planning the means by which a particular quality (attention, memory, imagination, thinking) can be developed, taking into account the individuality of each child and the available knowledge
- Construction of an interdisciplinary (integral) basis for training in a developmental course.
- A gradual complication of the material, a gradual increase in the volume of work, an increase in the level of independence of children.
- Acquaintance with the elements of theory, teaching methods of reasoning, self-argumentation of choice.
- Integration of knowledge and methods of cognitive activity, mastering its generalized techniques.
- Evaluation of the results of the developmental course according to the developed criteria, which should include the child (self-assessment, self-control, mutual control).
1.
6
Contents of the program
A brief description of the sections and topics of the lesson (the sections correspond to a certain logical operation that the children will be taught in the lesson):
1. Analysis - synthesis.
The goal is to teach children to divide the whole into parts, to establish a connection between them; teach mentally to combine parts of the subject into a single whole.
Games and exercises: finding a logical pair (cat - kitten, dog -? (Puppy)). Complement the picture (pick up a patch, add a pocket to the dress). Search for opposites (light - hard, cold - hot). Work with puzzles of varying complexity. Laying out pictures from counting sticks and geometric shapes.
2. Comparison.
The goal is to teach mentally to establish the similarities and differences of objects according to essential characteristics; develop attention, perception of children. Improve spatial orientation.
Games and exercises: consolidation of concepts: large - small, long - short, low - high, narrow - wide, higher - lower, further - closer, etc. Operating with the concepts of "the same", "the most". Search for similarities and differences in 2 similar pictures.
3. Restriction.
The goal is to teach you to single out one or more objects from a group according to certain criteria. Develop children's observation skills.
Games and exercises: "circle only the red flags with one line", "find all non-circular objects", etc. Exclusion of the fourth superfluous.
4. Generalization.
The goal is to teach mentally to combine objects into a group according to their properties. Contribute to the enrichment of vocabulary, expand the everyday knowledge of children.
Games and exercises for operating with generalizing concepts: furniture, dishes, transport, vegetables, fruits, etc.
5. Systematization.
The goal is to teach how to identify patterns; expand the vocabulary of children; to teach to tell from the picture, to retell.
Games and exercises: magic squares (pick up the missing part, picture). Drawing up a story based on a series of pictures, arranging pictures in a logical sequence.
6. Classification.
The goal is to teach how to distribute objects into groups according to their essential characteristics. Consolidation of generalizing concepts, free handling of them.
7. Inferences.
The goal is to teach judgments to make a conclusion. Contribute to the expansion of everyday knowledge of children. Develop imagination.
Games and exercises: search for positive and negative in phenomena (for example, when it rains, it nourishes the plants - this is good, but the bad thing is that in the rain a person can get wet, catch a cold and get sick). Evaluation of the fidelity of certain judgments (“the wind blows because the trees are swaying.” Right?). Solving logical problems.
1.7 Expected results
Planned results:
Children should know:
- principles of building patterns, properties of numbers, objects, phenomena, words;
- principles of the structure of puzzles, crosswords, teawords, labyrinths;
- antonyms and synonyms;
- names of geometric shapes and their properties;
- the principle of programming and drawing up an algorithm of actions.
Children should be able to:
- determine patterns and perform the task according to this pattern, classify and group objects, compare, find general and particular properties, generalize and abstract, analyze and evaluate their activities;
- by reasoning, solve logical, non-standard problems, perform creative search, verbal and didactic, numerical tasks, find the answer to mathematical riddles;
- quickly and correctly answer the questions posed during the warm-up;
- perform tasks for training attention, perception, memory
- perform graphic dictations, be able to navigate in a schematic representation of graphic tasks;
- be able to set a goal, plan the stages of work, achieve a result by one's own efforts.
Method of checking work results : generalizing lessons after each section and 2 diagnostics (initial (September) and final (May)) of the level of mastering the operations of logical thinking.
Logic tasks, like mathematics, is called "gymnastics of the mind." But unlike mathematics, logic tasks- this is entertaining gymnastics, which in a fun way allows you to test and train thought processes, sometimes from an unexpected angle. To solve them, you need quick wits, sometimes intuition, but not special knowledge. Logic problem solving is to thoroughly analyze the condition of the problem, to unravel the tangle of contradictory connections between characters or objects. Logic tasks for children- these are, as a rule, whole stories with popular actors, into which you just need to get used to, feel the situation, visualize it and catch connections.
Even the most complex logic problems do not contain numbers, vectors, functions. But the mathematical way of thinking is necessary here: the main thing is to comprehend and understand the condition logical task... The most obvious solution on the surface is not always the right one. But more often than not, solving a logic problem turns out to be much easier than it seems at first glance, despite the confusing condition.
Interesting logic problems for children in a variety of subjects - mathematics, physics, biology - arouse their keen interest in these academic disciplines and help in their meaningful study. Logic tasks weighing, transfusing, tasks for non-standard logical thinking will help to solve everyday problems in a non-standard way in everyday life.
In the process of solving logic tasks you will get acquainted with mathematical logic - a separate science, otherwise called "mathematics without formulas". Logic as a science was created by Aristotle, who was not a mathematician, but a philosopher. And logic was originally part of philosophy, one of the methods of reasoning. In his work "Analytics" Aristotle created 20 schemes of reasoning, which he called syllogisms. One of his most famous syllogisms is: “Socrates is a man; all people are mortal; means Socrates is mortal. " Logic (from Old Greek. Λογική - speech, reasoning, thought) is the science of correct thinking, or, in other words, the "art of reasoning."
There are certain tricks solving logical problems:
way of reasoning, with the help of which the simplest logical problems are solved. This method is considered the most trivial. In the course of the solution, reasoning is used that consistently takes into account all the conditions of the problem, which gradually lead to a conclusion and the correct answer.
way of tables, used in solving text logic problems. As the name suggests, solving logical problems consists in constructing tables that allow you to visualize the condition of the problem, control the process of reasoning and help you draw the correct logical conclusions.
way of graphs consists in enumerating possible options for the development of events and the final choice of the only correct solution.
block diagram method- a method widely used in programming and solving logical transfusion problems. It consists in the fact that, first, operations (commands) are allocated in the form of blocks, then the sequence of execution of these commands is established. This is a block diagram, which is essentially a program, the execution of which leads to the solution of the task.
billiards way follows from the theory of trajectories (one of the branches of the theory of probability). To solve the problem, it is necessary to draw a billiard table and interpret the actions by the movements of the billiard ball along different trajectories. In this case, it is necessary to keep records of possible results in a separate table.
Each of these methods is applicable to solving logical problems from different areas. These seemingly complex and scientific techniques can be easily used in solving logic problems for 1, 2, 3, 4, 5, 6, 7, 8, 9 classes.
We present to you the most diverse logical tasks for 1, 2, 3, 4, 5, 6, 7, 8, 9 grades. We have selected the most interesting logic problems with answers, which will be interesting not only for children, but also for parents.
- pick up for the child logic tasks according to his age and development
- take your time to open the answer, let the child find himself logical solution tasks... Let him come to the right decision on his own and you will see what pleasure and delight he will have when his answer coincides with the given one.
- in progress solving problems on logic leading questions and indirect clues indicating the direction of thinking are permissible.
With our selection logical problems with answers you will really learn to solve logic problems, broaden your horizons and significantly develop logical thinking. Go for it !!!
Solving logical problems - the first step to child development.
E. Davydova
Logic is the art of coming to an unpredictable conclusion.
Samuel Johnson
Without logic, it is almost impossible to bring into our world ingenious finds of intuition.
Kirill Fandeev
A person who thinks logically stands out nicely against the background of the real world.
American dictum
Logic is the morality of thought and speech.
Jan Lukasiewicz
These tasks can be set to children on the way to school, on a trip, or by organizing a competition at a children's party. Few people will be able to immediately answer the question, so you should gradually give small hints, this will make the solution more fun and interesting.
We hope that you will not just put your child at the computer so that he can see all the answers at once. Do not forget that no car can replace a son or daughter's parental love and attention.
1. What word is always spelled wrong? (A joke task.)
Correct answer
2. How many months in a year have 28 days?
All months
Correct answer
3. At what speed should the dog move (within the limits possible for it) so as not to hear the ringing of a frying pan tied to its tail?
From zero. The dog needs to stand still
Correct answer
4. The dog was tied to a ten-meter rope and walked two hundred meters in a straight line. How did she do it?
Her rope was not tied to anything
Correct answer
5. How to jump off a 10-meter ladder and not hurt yourself?
You need to jump from the bottom step
Correct answer
6. What can you see with your eyes closed?
Correct answer
7. What does not burn in fire and does not sink in water?
Correct answer
8. Whom do Australians call sea wasp?
Correct answer
9. What should you do when you see a green man?
Cross the street (this is a drawing on a green traffic light)
Correct answer
10. Moscow used to be called white stone. And which city was called black?
Chernihiv
Correct answer
11. Inhabitants of medieval Europe sometimes tied wooden chocks to the soles. For what purpose did they do it?
For protection from dirt, because there was no sewage system and the slop was poured directly onto the street
Correct answer
12. In what process did water replace the sun, after 600 years it was replaced by sand, and after 1100 years all of them were replaced by a mechanism?
In the process of measuring time - hours
Correct answer
13. In the old days, barns were built on the outskirts, away from dwellings. For what purpose?
To prevent the fire from destroying food supplies
Correct answer
14. Under Peter I, an eagle was depicted on the coat of arms of the Russian Empire, holding maps of the four seas in its paws. List them.
White, Caspian, Azov, Baltic
Correct answer
15. The name of which Germanic tribe gave the name to the whole European country?
The Germanic tribe of Franks gave the name to France
Correct answer
16. Why don't polar bears eat penguins in the wild?
Polar bears live at the North Pole, while penguins live at the South Pole.
Correct answer
17. Not wanting to admit that the Red Army could defeat them, the Germans argued that General Moroz, General Dirt and General Mouse won the Great Patriotic War. With regard to frost and dirt, everything is clear. But what does the mouse have to do with it?
Mice gnawed at the electrical wiring of German tanks
Correct answer
18. Name five days without naming numbers (1, 2, 3, ..) and names of days (Monday, Tuesday, Wednesday ...)
The day before yesterday, yesterday, today, tomorrow, the day after tomorrow
Correct answer
19. Thirty-two warriors have one commander.
Teeth and tongue
Correct answer
20. Twelve brothers
They roam one after another,
Do not bypass each other.
Correct answer
21. What is the correct way to say: “I don’t see the white yolk” or “I don’t see the white yolk”?
The yolk is usually yellow
Correct answer
22. Is it possible to light an ordinary match under water so that it burns out to the end?
Yes, in a submarine
Correct answer
23. When is the best time for a black cat to get into the house?
When the door is open
Correct answer
24. Two fathers and two sons walked, they found three oranges. They began to divide - all got one by one. How could this be?
Correct answer
25. What kind of dishes can you not eat anything from?
From empty
Correct answer
26. A small, grayish one looks like an elephant. Who is this?
Baby elephant
Correct answer
27. Which hand is better for stirring tea?
The one in which the spoon
Correct answer
28. They knock, knock - they don't tell you to get bored.
They walk, they walk, and everything is right there.
Correct answer
29. Very fast two knights
They carry me through the snow - Through the meadow to the birch,
Draw two strips.
Correct answer
30. When is a person in a room without a head?
When he pokes her out of the room (for example, out the window).
Correct answer
31. What question cannot be answered “yes”?
Do you sleep?
Correct answer
32. What question cannot be answered “no”?
Correct answer
33. When can the net draw out water?
When the water freezes and turns to ice.
Correct answer
34. Bold as ...,
insidious as ...,
cowardly like ...
cunning as ...,
evil as ...,
hungry like ...
hardworking like ...
true as ...,
stubborn as ...
stupid like ...
quiet as ...,
free as….
Lion, snake, hare, fox, dog, wolf, ant, dog, donkey, ram, mouse, bird
Correct answer
35. How do day and night end?
By the soft sign
Correct answer
36. The magpie flies, and the dog sits on its tail. Could it be?
Yes, the dog sits on its own tail, next to the magpie flies
Correct answer
37. What should be done to keep five guys in one boot?
Each of them take off a boot
Correct answer
38. How much is 2 + 2 * 2?
Correct answer
39. In what month the chatty Svetochka speaks least of all?
February is the shortest month
Correct answer
40. What belongs to you, but others use it more than you do?
Correct answer
41. How to find last year's snow?
Go outside immediately after the start of the new year.
Correct answer
42. What word always sounds wrong?
Correct answer
43. A man has one, a cow has two, a hawk has none. What's this?
Correct answer
44. A man is sitting, but you cannot sit in his place, even if he gets up and leaves. Where is he sitting?
On your knees
Correct answer
45. What stones are there in the sea?
Correct answer
46. What sign should be placed between 4 and 5 in order for the result to be more than 4 and less than 5?
Correct answer
47. Can a rooster call itself a bird?
No, because he cannot speak.
Correct answer
48. What disease on earth has no one sick?
Correct answer
49. Is it possible to predict the score of any match before it starts?
Correct answer
50. What can be cooked but not eaten?
Correct answer
51. What number will decrease by a third if it is turned over?
Correct answer
52. One corner was sawed off at a square table in a straight line. How many corners does the table have now?
Correct answer
53. Which knot cannot be untied?
Railway
Correct answer
54. What is the front of the cow and the back of the bull?
Correct answer
55. What is the worst river?
Correct answer
56. What has no length, depth, width, height, but can be measured?
Temperature, time
Correct answer
57. What are all people on earth doing at the same time?
Are getting older
Correct answer
58. Two people were playing checkers. Each played five games and won five times. Is it possible?
Both people played different games with other people.
Correct answer
59. How can a thrown egg fly three meters and not break?
You need to throw an egg more than three meters, then the first three meters it will fly intact.
Correct answer
60. The man was driving a large truck. The headlights on the car were not on. There was no moon either. The woman began to cross the road in front of the car. How did the driver manage to see her?
It was a bright sunny day.
Correct answer
61. Where is the end of the world?
Where the shadow ends.
Correct answer
62. Man learned to build suspension bridges from spiders, from cats he adopted a diaphragm in a camera and reflective road signs. What invention came from snakes?
Correct answer
63. What can you easily pick up from the ground, but you can't throw it far?
Poplar fluff.
Correct answer
64. What kind of comb can you comb your head with?
Petushin.
Correct answer
65. What do they give up when they need it, and raise it up when there is no need for it?
Correct answer
66. What can travel the world, staying in the same corner?
Postage Stamp.
Correct answer
67. You are sitting in an airplane, there is a horse in front of you, a car behind you. Where are you at?
On the carousel
Correct answer
68. What notes can be used to measure the distance?
Correct answer
69. What won't fit in the biggest pot?
Its cover.
Correct answer
70. Russian riddle. A wooden river, a wooden boat, and a wooden smoke is streaming over the boat. What's this?
Correct answer
71. A satellite makes one revolution around the Earth in 1 hour 40 minutes, and another in 100 minutes. How can this be?
One hour and forty minutes equals one hundred minutes.
Correct answer
72. Name at least three animals that Moses took into his ark?
Prophet Moses did not take animals into the ark, righteous Noah did it.
Correct answer
73. The boy carried one kilogram of iron in one hand, and the same amount of fluff in the other. What was harder to carry?
The same.
Correct answer
74. In 1711, in each regiment of the Russian army, a new division of 9 people appeared. What is this unit?
Regimental Orchestra.
Correct answer
Plane crashes.
Correct answer
76. There is a story about a little boy who, having received a New Year's gift, asked his mother: “Please take off the lid. I want to stroke a present. " What is this gift?
Turtle
Correct answer
77. What animals always sleep with their eyes open?
Correct answer
78. It is known that in due time silkworm eggs were exported from China on pain of death. And what animal was taken out of Afghanistan in 1888 with the same risk?
Afghan hound.
Correct answer
79. What insects are domesticated by humans?
Correct answer
80. A problem invented by the learned monk and mathematician from Ireland Alcuin (735-804).
The peasant needs to transport a wolf, a goat and a cabbage across the river. But the boat is such that only a peasant can fit in it, and with him either one wolf, or one goat, or one cabbage. But if you leave the wolf with the goat, the wolf will eat the goat, and if you leave the goat with the cabbage, then the goat will eat the cabbage. How did the peasant transport his cargo?
Solution 1: Clearly you have to start with the goat. The peasant, having transported the goat, returns and takes the wolf, which he transports to the other side, where he leaves it, but he takes the goat and carries it back to the first bank. Here he leaves her and transports the cabbage to the wolf. Followed then, returning, he transports a goat, and the crossing ends safely. Solution 2: First, the peasant again transports the goat. But the second can take the cabbage, take it to the other side, leave it there and return the goat to the first bank. Then transport the wolf to the other side, return for the goat and again take it to the other side.
Correct answer
81. In the old days in Russia, married women wore a headdress kokoshnik, the name of which came from the word "kokosh", meaning an animal. Which?
Chicken (remember what she says when she rushes?).
Correct answer
82. Why can't a porcupine drown?
He has hollow needles.
Correct answer
83. What is the fifth largest country in terms of area after Russia, China, Canada and the United States?
Brazil.
Correct answer
84. A man went to the market and bought a horse there for 50 rubles. But he soon noticed that the price of horses had risen and sold it for 60 rubles. Then he realized that he had nothing to ride, and bought the same horse for 70 rubles. Then he wondered how not to get a scolding from his wife for such an expensive purchase, and sold it for 80 rubles. What did he earn as a result of the manipulation?
Answer: -50 + 60 - 70 + 80 = 20
Correct answer
85. The only bird that has auricles?
Correct answer
86. Two at the same time approached the river. A boat that can be crossed can only hold one person. And yet, without assistance, everyone crossed the boat to the other side. How did they do it?
They sailed from different shores.
Correct answer
87. In Chinese, the combination of three characters for "tree" means the word "forest". And what does the combination of two hieroglyphs "tree" mean?
Correct answer
88. Residents of Kansas are very fond of Russian nuts. What is it if it is known that we can find them in any market?
Correct answer
89. The Romans introduced a revolutionary innovation to the fork design - all subsequent models were just variations of the solution found. And what was the fork before this innovation?
One-toothed.
Correct answer
90. Chinese martial artists used to say that a fight is for fools, for smart ones it is a victory. And what, in their opinion, is for the wise?
Correct answer
91. What is the native language for the largest number of people.
Chinese.
Correct answer
92. In Ancient Rus they were called broken numbers. What are they called nowadays?
Correct answer
93. A brick weighs two kilograms and a floor of a brick. How many kilograms does a brick weigh?
We put a brick on one pan. On the other, we put a 2-kilogram weight and a half-brick. Now let's break a whole brick in half and remove half a brick from each pan. We get: on the left half a brick, on the right - a 2-kilogram weight. That is, half a brick weighs two kilograms. And two half bricks, that is, a whole brick, weighs four kilograms.
Correct answer
94. For some reason, these people, returning to their homeland, brought with them branches of exotic plants, for which they received their nickname. What kind of people are they?
Pilgrims, they brought palm leaves.
Correct answer
95. In terms of production, bananas rank first in the world, followed by citrus fruits. What are the fruits in third?
Correct answer
96. In the American state of Arizona, they began to protect the desert from thieves. They steal that without which the desert is threatened with desolation and devastation. What do the thieves take out of the desert?
Correct answer
97. Name the plant with the largest fruits.
Correct answer
98. Neither fish nor meat - what was this Russian proverb originally about?
Correct answer
99. In Spain they are called the Portuguese, in Prussia - the hares. And what are they called in Russia?
Cockroaches.
Correct answer
100. Whom do the Malays catch with the help of a locked bamboo cage with a live pig inside?
Pythons, after eating the pig, they could no longer get out of the cage.
Correct answer
101. A hedgehog has 4 g, a dog - 100 g, a horse - 500 g, an elephant - 4-5 kg, a man - 1.4 kg. What?
Brain mass.
Correct answer
102. In 1825, the streets of Philadelphia were cleared of litter by pets. Which ones?
Pigs.
Correct answer
103. What dish did Marco Aroni invent in the 17th century?
Pasta.
Correct answer
104. What does any cosmonaut lose in flight?
Correct answer
105. As you know, all native Russian female (full) names end either in A or Z: Anna, Maria, Olga, etc. However, there is one female name that does not end in either A or Z. Name it.
Correct answer
106. Gallic priests found a reliable way to quickly mobilize soldiers in case of war. For this, they sacrificed only one person. Which one?
The last to come.
Correct answer
107. Once in the city of Nice, a competition was held for the most hardy smoker. One of the participants set a record by smoking 60 cigarettes in a row. However, he did not receive the prize. Why?
Correct answer
108. A person has twelve pairs of ribs. And who has more than three hundred edges?
Correct answer
109. In the mouth - a pipe, in the hand - a tambourine, under the arm - mug. This is how buffoons were portrayed in Russia. As for the pipe and tambourine, everything is clear, but what is a mug?
Correct answer
110. Everyone knows that "you cannot wash dirty linen in public." And what, after all, was supposed to be done with him if he couldn't bear it?
Correct answer
111. Where did the Russian men wear hats and mittens, regardless of the season?
Correct answer
112. How is stickleback fish similar to birds?
She builds nests, laying eggs there.
Correct answer
113. Which grass is the tallest?
Correct answer
114. Name an agricultural crop that burns 90% and throws away 10%.
Correct answer
115. The Greeks used this to protect certain parts of their body. It was crafted from sandalwood bark. Name it.
Sandals.
Correct answer
116. The first greenhouses appeared in France. What do you think for what?
For growing oranges (orange - orange).
Correct answer
117. The owner of the largest horn is a white rhinoceros (up to 158 cm). Which animal has the softest horns?
Correct answer
118. This is what football referees used before the whistle was used.
Bell.
Correct answer
119. What is considered dirty when it is white and clean when it is green?
Blackboard.
Correct answer
120. In practice, when moving along a curve, this ball makes 5000 revolutions per minute, and when moving in a straight line, more than 20,000 revolutions per minute. Where is this ball located?
In a ballpoint pen.
Correct answer
121. The great Hippocrates was asked: "Is it true that genius is a disease?" "Certainly," Hippocrates replied, "but very rare." What other property of this disease was noted with regret by Hippocrates?
Not contagious.
Correct answer
122. What was the name of the city in England, where in 1873 the Indian game, popular to this day, was first demonstrated?
Badminton.
Correct answer
123. Where, judging by the name, the ancient Slavs fastened the cover for hunting edged weapons?
On the foot. This is the scabbard.
Correct answer
124. Three painters had a brother Ivan, but Ivan had no brothers. How could this be?
Ivan had three sisters.
Correct answer
125. The Russian princes had various nicknames that came from the names of cities (Vladimirsky, Chernigovsky, Galitsky), from bright personal qualities (Udaloi, Wise, Kalita). What nickname did Prince Vsevolod receive, who had twelve children?
Vsevolod the Big Nest.
Correct answer
126. In 1240, a population census was carried out for the first time in Kievan Rus. Who did it and for what purpose?
Genghis Khan (to collect tribute from the population).
Correct answer
127. It was 988 ... A large crowd of inhabitants of ancient Kiev was moving towards the Dnieper for some reason. What was the name of the road along which the townspeople walked?
988 is the year of the baptism of Rus. The street is called Khreshchatyk.
Correct answer
128. Russia consisted of Great Russia (Russia proper), Little Russia (Ukraine), White Russia (Belarus). And what was the name of Manchuria, which was part of this state?
Yellow Russia.
Correct answer
129. The Italian flag is red-white-green. Which cutaway berry helped the Italians choose these colors?
Correct answer
130. Socrates did this "in order to sharpen thought." Seneca did the same. Horace was thus cured of a serious illness. Suvorov was a big fan of this. Both A.S. Pushkin and L.N. Tolstoy loved to do this. What did they do?
We walked barefoot.
Correct answer
131. What was the name of a philosopher in Russia earlier?
Wise.
Correct answer
132. What flower was considered a symbol of royal power?
Correct answer
133. If the Turks wanted to say “guard the village”, they said “kara avyl”. How do we speak now?
Correct answer
134. Ancient Romans wore a tunic. And what did they wear when the cold came?
Several tunics, one on top of the other.
Correct answer
135. How will “shoes” be in Tatar?
Correct answer
136. We, basically, use only the beginning of this proverb, and its end: "... just choked on his tail"?
I ate the dog.
Correct answer
137. Say in Danish “Ole, close your eyes”.
Ole Lukkoye.
Correct answer
138. Barbarians were easily recognized by this garment.
Correct answer
139. Which literary character had 300-year-old calluses?
Old Man Hottabych.
Correct answer
140. These three brothers can be called architects.
Three pigs.
Correct answer
141. As you know, grandfather Mazai saved many birds with one stone. Name the person who saved eighteen pigeons and a sparrow during a fire.
Uncle Styopa.
Correct answer
142. What words does a proverb begin if its ending sounds like this: "... and cows lay eggs"?
They say that chickens are milked ...
Correct answer
143. What words does a proverb begin if its ending sounds like this: "... there will be Great Lent"?
Every day is not Sunday…
Correct answer
144. How does the proverb begin: "... the stump is great, but the duplist"?
Small spool but precious.
Correct answer
145. Everyone knows the expression "Take care of it like the apple of your eye." And what is the "apple of an eye"?
Eye pupil.
Correct answer
146. This word literally means "what will happen after the morning." What is this word?
In the morning - tomorrow.
Correct answer
147. He really wanted to become a real boy and eventually became one. Who is he?
Pinocchio.
Correct answer
148. What fairytale hero from birth spoke three languages?
Dragon.
Correct answer
149. In Russia it was eaten everywhere, the Romans called it a stinking plant, and Pythagoras called it the king of spices. Name it.
Correct answer
150. Before the advent of the potato, it was the main food for the poor in Europe. And we know this better from a short work with six characters.
Correct answer
151. What kind of plant is this that personifies both a relative and an adoptive relative?
Coltsfoot.
Correct answer
152. Among all garden weeds, according to traditional medicine, it is very useful, especially if you prepare a salad with it ...
Correct answer
153. Russian riddle: "The girl is red, and the heart is stone." What's this?
Correct answer
154. Which peaceful ships have not captains, but commanders?
Space.
Correct answer
155. What is the most popular type of transport for logging in hard-to-reach regions of Asia?
Correct answer
156. Once in the Russian army there was an officer by the name of Sieverst-Mehring, who became famous, like Baron Munchausen, for his irrepressible imagination. What phraseological unit was born in connection with his name?
Lies like a gray gelding.
Correct answer
157. He has four, but if you cut them all off, then he will have as many as eight. What is it about?
On the corners of a quadrangle.
Correct answer
158. Catherine II bought works of art all over the world to place them in a “secluded refuge”. What do we call it now?
Correct answer
159. Julius Caesar ordered his soldiers to decorate their shields and weapons with jewels. What for?
That it was a pity to quit.
Correct answer
160. What is the difference between running and walking? Before answering this question, remember that running can be slower than walking, and that there is even running in place.
Running differs from walking not in speed of movement. When walking, our body always touches the ground with some point of the legs. While running, there are moments when our body is completely separated from the ground, not touching it at any point.
Correct answer
161. All victims of accidents in the city were sent to the hospital in Kukuev. Most of all there were drivers and passengers injured in road accidents. To reduce their numbers, the city has made it mandatory to wear seat belts. Drivers and passengers began to wear these belts, but the number of accidents remained unchanged, and the number of injured people who were admitted to the hospital even increased. Why?
Wearing seat belts has reduced the number of fatalities in road accidents. Many people who would have died without a seat belt (and ended up in morgues) survived, but were injured and needed treatment. Therefore, the number of people admitted to the hospital has increased.
Correct answer
162. There are two sentries at the roadside. One looks to one side of the road, and the other to the opposite, but at the same time they see each other. How can this be? Options with reflections, etc. - excluded.
Although the sentries are looking in opposite directions, they are not standing back to back, but facing each other.
Correct answer
163. If it rains at 12 o'clock in the morning, can you expect to see sunny weather in 72 hours?
No, as it will be midnight again in 72 hours.
Correct answer
164. There is a round deep lake 200 meters in diameter and two trees, one of which grows on the shore near the water, the other - in the center of the lake on a small island. A person who does not know how to swim needs to get over to the island using a rope, the length of which is slightly more than 200 meters. How can he do it?
Having tied the rope with one end to a tree growing on the shore, it is necessary to go around the lake with a rope stretched over the water and tie the other end of the rope to the same tree. As a result, a double rope will be stretched between the trees to cross to the island.
Correct answer
165. A man lives on the 17th floor. He takes the elevator to his floor only in rainy weather or when one of the neighbors is taking the elevator with him. If the weather is fine and he is alone in the elevator, then he goes to the 9th floor, and then to the 17th floor he walks up the stairs ... Why?
Correct answer
166. One person was asked:
How old are you?
“Decent,” he replied.
- I am almost six hundred times older than some of my relatives. How can this be?
For example, if a person is 50 years old, and his grandson or granddaughter is 1 month old.
Correct answer
167. People who came to one village were often surprised at the local fool. When he was offered a choice between a shiny 10-ruble coin and a crumpled hundred-ruble bill, he always chose a coin, although it costs ten times less than a bill. Why did he never choose the bill?
He was not at all stupid: he understood that while he was choosing a ten-ruble coin, people would offer him money to choose from, and if he chose a hundred-ruble bill, the offers of money would stop and he would not receive anything.
Correct answer
168. The day before yesterday Petya was 17 years old. He will turn 20 next year. How can this be?
If the current day is January 1, and Petya's birthday is December 31. The day before yesterday (December 30) he was still 17 years old, yesterday (December 31) he turned 18, this year he will turn 19, and next year 20.
Correct answer
169. One king wanted to remove his prime minister, but did not want to offend him too much. He called the Prime Minister to his place, put two sheets of paper in his portfolio with him and said: “On one sheet I wrote 'Go away', and on the second - 'Stay.' The sheet that you pull out will decide your fate. " The Prime Minister guessed that both sheets of paper read "Go away." How, however, did he manage to keep his place under these conditions?
The Prime Minister pulled out a piece of paper and, without looking at it, rolled a ball out of it - and swallowed it. Since the remaining sheet read -Go away-, the king had to admit that the swallowed sheet read -Stay-.
Correct answer
170. One gentleman, showing his friend a portrait painted by his order by one artist, said: "I have no sisters or brothers, but this man's father was the son of my father."
The portrait shows the gentleman's son.
Correct answer
171. There are 8 benches in the park. Three painted. How many benches are there in the park?
Correct answer
172. The thermometer shows plus 15 degrees. How many degrees will two such thermometers show?
15 degrees.
Correct answer
173. The loaf was cut into three parts. How many incisions were made?
Two cuts.
Correct answer
174. What is lighter than 1 kg of cotton wool or 1 kg of iron?
The same.
Correct answer
175. The truck was driving to the village. On the way, he met 4 cars. How many cars were driving to the village?
Correct answer
176. Twice will be born, once dies. Who is this?
Chick.
Correct answer
177. What can't you pick up by the tail from the floor?
Correct answer
178. What always increases and never decreases?
Correct answer
179. The more you take from it, the more it becomes. What's this?
Correct answer
180. The 9-storey building has an elevator. 2 people live on the first floor, 4 people on the second, 8 people on the third, 16 on the fourth, 32 on the fifth, and so on. What's the most pressing button in the elevator in this house?
Ground floor button.
Correct answer
181. Something goes uphill, then downhill, but remains in place?
Correct answer
182. Seven sparrows were sitting on a tree, one of them was eaten by a cat. How many sparrows are left on the tree?
None: the surviving sparrows scattered.
Correct answer
183. Guests have come to you, and in the fridge there is a bottle of lemonade, a bag of apple juice and a bottle of mineral water. What will you discover first?
Refrigerator.
Correct answer
184. What Russian city flies?
Correct answer
185. What is not eaten raw, but boiled - thrown away?
Bay leaf.
Correct answer
186. What two words in Russian are written with three letters "e" in a row?
Long-necked and snake-eater.
Correct answer
187. When the Europeans brought her to Tahiti, the islanders, who had never seen anything like it before, christened her a pig with teeth on its head. What do we call it?
Correct answer
188. There are monkey schools in Thailand. What do they teach?
Collect coconuts.
Correct answer
189. How, according to scientists, does a crocodile get rid of excess salts in the body?
Correct answer
190. One of the Japanese airlines paints huge eyes on the nose of its planes. What for?
Scare birds away.
Correct answer
191. Why do birds choose a cold day for departure in autumn, and arrive in spring on a warm one?
Choose a tailwind.
Correct answer
192. According to the writer O'Henry, she is the only animal into which nails are driven. Who is this?
Correct answer
193. From the skin of this particular animal, files were first made, which were used to polish wood and even marble.
Correct answer
194. What animal ranks second after a person in terms of the number of images on pedestals?
Correct answer
195. The absence of what organ does not allow sharks to stop even for a moment, otherwise they will simply drown?
Swimming bladder.
Correct answer
196. Who has teeth in the stomach?
Correct answer
197. Until the XVI century. only white and yellow varieties of it existed in nature. However, Dutch breeders, admirers of the Duke of Orange, have developed a currently known patriotic color variety. What are we talking about?
About carrots.
Correct answer
198. As the name of this country suggests, it should consist mainly of plains and steppes. Nevertheless, most of the plains no longer belong to it, and at present about half of its territory is occupied by mountains, hills and forests. What country is it?
Poland (from the word field).
Correct answer
199. The territory of Finland is 8% covered with lakes. Although it is called the country of a thousand lakes (and there are much more of them), the primacy belongs to another. Which?
Correct answer
200. What metal is found in nature less often than platinum or uranium, but until recently it was in almost every home?
Mercury in a thermometer.
Correct answer
201. In which state of the United States there is one woman for every 50 men?
Correct answer
202. There is something so fragile that even saying its name, you break it. What's this?
Correct answer
203. In 1086, the sister of Vladimir Monomakh opened a school at one of the Kiev monasteries. How did this school differ from all those that existed in Russia before?
Correct answer
204. Where were potatoes first discovered?
Correct answer
205. How to write "nineteen", and then, removing one, get
"twenty"?
Correct answer
206. Feed him and he will come to life. Get him drunk and he dies. What it is?
Correct answer
207. That has 5 fingers, but at the same time is not a living being.
Glove.
Correct answer
208. I am nothing, but I have a name. Sometimes I'm big, sometimes
small and cannot exist alone. Who am I?
Correct answer
209. What does half of an orange look like the most?
For the second half.
Correct answer
210. What part of the bookcase consists of half a consonant letter?
Correct answer
211. How many ends do three sticks have? Four and a half? two and a quarter?
Three have 6, four and a half have 10, two and a quarter have 6.
Correct answer
212. How many eggs can you eat on an empty stomach?
One (the rest will no longer be on an empty stomach).
Correct answer
213. What word begins with three letters "G" and ends with three letters "I"?
Trigonometry.
Correct answer
214. What is the arithmetic mean between a bicycle and a motorcycle?
Correct answer
215. Small, gray, does it look like an elephant?
Baby elephant.
Correct answer
216.there are two dombras,harpsthere are five of them, the guitar has six. How many of them does a piano have?
Seven (octaves).
Correct answer
217. What kind of baby is born with a mustache?
For example, a kitten.
Correct answer
218. When can a person rush with the speed of a racing car?
When he is in it.
Correct answer
219. What do elephants have and what other animals do?
Correct answer
220. To whom do all people take off their hats?
In front of the hairdresser.
Correct answer
221. How to write a mousetrap in five letters?
Correct answer
222. My father's son, and not my brother?
Correct answer
223. What kind of fabric can not be sewn into a shirt?
From the railway.
Correct answer
224. What city is in the compote?
Raisin (A city in Ukraine, in the Kharkiv region).
Correct answer
225. There were 20 bulbs in the lamp, 5 of them burned out. How many bulbs are left?
Twenty bulbs (15 working and 5 burned out).
Correct answer
226. Dad caught 3 fish in 10 minutes while fishing. How long will it take for him to catch 10 more fish?
The problem has no clear answer.
Correct answer
227. There were 9 rolls on the tray. 9 girls took a bun each. But there was only one bun left on the tray. How did this happen?
The last girl took the bun along with the tray.
Correct answer
228. Vasya is 5 years old. And Anya is 9 years old. What is the age difference between them in three years?
Four years (the age difference does not change).
Correct answer
229. From the forest, Misha brought 2 porcini mushrooms, 3 boletus boletus, 4 amanita and 5 russula for mushroom soup to his grandmother. How many mushrooms will grandmother need for soup?
10 mushrooms, fly agaric is an inedible mushroom.
Correct answer
230. Plane, steamer, balloon, helicopter. What word is superfluous here?
Steamer (does not fly).
Correct answer
231. Two people entered the entrance at the same time. One has an apartment on the 3rd floor, the other has an apartment on the 9th. How many times will the first one get there faster than the second one?
4 times, because the 1st needs to overcome 2 gaps between the floors, and the 2nd - 8.
Correct answer
232. What object, made by man before the 20th century, can move faster than sound?
The tip of the whip. We hear a characteristic click (pop) precisely because the tip overcomes the sound barrier.
Correct answer
233. A car wheel is rolling to the right; its rim turns clockwise. In which direction does the air move inside the rubber tire of the wheel - towards the rotation of the wheel or in the same direction?
The air inside the tire moves from the compression point in both directions - back and forth.
Correct answer
234. What is in first place in Russia, and in second in France?
Correct answer
235. A camel withstands a load of 10 poods for an hour. How long will it last for a load of 1000 poods?
None. The camel cannot bear that weight.
Correct answer
236. Why are riddles dangerous for the head?
Because people are puzzled over him.
Correct answer
237. What can snow and a lilac bush have in common?
Color. Lilac flowers are also white.
Correct answer
238. What does the watchman do when a sparrow sits on his head?
Correct answer
239. Where are cities without houses, rivers without water and forests without trees?
On a geographic map
Correct answer
240. In the name of which side of the world there are one hundred and one letters?
Correct answer
241. Who speaks all languages?
Correct answer
242. They walk with a load, stop without a load.
Clock with weights.
Correct answer
243. Who has a mustache longer than legs?
Cancer, cockroach.
Correct answer
244. What was "tomorrow" and will be "yesterday"?
Correct answer
245. Six legs, two heads, and one tail. What's this?
Horse rider.
Correct answer
246. What clock shows the correct time only twice a day?
That stopped.
Correct answer
247. Once the guys gathered for a picnic, only 6 people. They looked, and instead of 6 apples they took 5. How to divide apples equally among all, so that no one was offended? They cannot be cut or broken.
It is necessary to cook compote from apples.
Correct answer
248. If Erica lives in Washington, and Tina lives in Buenos Aires, then where does Tai live?
In Pekin. The names of the people are part of the names of the country in the capital of which each of them lives.
Correct answer
249. In 1849, a man went to California, where the gold rush was raging. He hoped to get rich by selling tents to gold diggers. However, the weather was fine, and the prospectors slept in the open air. Nobody bought tents. Nevertheless, the seller became rich, and his products are sold to this day. How did he do it and what was his name?
Correct answer
250. The spy sat in the bushes and assesses the situation at the checkpoint. An officer approaches, a sentry to him: "Password".
Officer: "26".
Sentry: "Review".
Officer: "13".
Sentry: "Come in."
The second one fits: "Password!" - "22".
"Review" - "11".
"Come in."
Well, the spy thinks he figured out the password system, runs to the sentry.
Sentry: "Password".
Spy: "100".
Sentry: "Review".
Spy: "50"
In general, they caught a spy. Which answer would be correct?
The correct answer is 3. This is the number of letters in the word one hundred.
Correct answer
251. For each of the following words, come up with a word that has the same meaning and begins with the letter K:
Wealth, Print, Universe, Lattice, Hearth, Comfort, Crown, Duke, Castle, Hammer.
1. Capital. 2. Brand. 3. Space. 4. Cell. 5. Fireplace. 6. Comfort. 7. Crown. 8. Prince. 9. Fortress. 10. Sledgehammer.
Correct answer
252. The doctor prescribed three tablets to the patient and ordered him to take them every half hour. How long will it take to take the pills?
At first glance, it may seem that a person will take the last pill in an hour and a half, because this is exactly three times for half an hour. In fact, he will take the last pill not in an hour and a half, but in an hour. The person immediately drinks the first pill. Half an hour passes. He takes the second pill. Another half hour passes. He takes the third pill. Therefore, the person will take the last pill one hour after the start of treatment.
Correct answer
253. What insect does the whole world applaud?
Correct answer
254. Is she red? - No, black. Why is she white? Because it's green. What's this?
Black currant.
Correct answer
255. How can you put two liters of milk in a liter jar?
Cook condensed milk from it.
Correct answer
256. A comic task. A hunter is riding on a bus, he sees a hare running. He fired. Where did he go?
To the police (Shooting in vehicles is prohibited).
Correct answer
257. Who is the jack of all trades?
Glover.
Correct answer
258. How to throw a tennis ball so that, having flown a short distance, it stops and starts moving in the opposite direction? In this case, the ball must not hit an obstacle, it must not be hit with something or tied to something.
Throw it up.
Correct answer
259. The ratio of the age of one boy to the age of another boy a few years ago was the same as it is now. What is this attitude?
One to one, that is, boys of the same age.
Correct answer
260. What is the largest number that can be written in four units?
Eleven to the eleventh power.
Correct answer
261. In the dense Murom forest, ten sources of dead water gush out from under the ground, they are numbered from No. 1 to No. 10.
From the first nine springs, everyone can take dead water, but spring number 10 is located in Koshchei's cave, into which no one, except Koshchei himself, can get.
The taste and color of dead water is no different from ordinary water, however, if a person drinks from any source, he will die. Only one thing can save him: if he drinks with poison from a source whose number is greater. For example, if he drinks from the seventh spring, then he must definitely drink poison No. 8, No. 9 or No. 10. If he drinks not the seventh poison, but the ninth, only poison No. 10 can help him. And if he immediately drinks the tenth poison, then nothing will help him.
Ivanushka the Fool challenged Koshchei to a duel. The conditions of the duel were as follows: each brings a mug of liquid with him and gives it to his opponent to drink. Koschey was delighted: “I will give poison number 10, and Ivan the fool will not be able to save himself! And I myself will drink the poison that Ivanushka the fool will bring me, I will drink it down with my tenth and I will be saved! "
On the appointed day, both opponents met at the agreed place. They honestly exchanged mugs and drank what was in them. It turned out that Koschey had died, but Ivan the Fool remained alive! How did it come about?
Ivanushka gave Kashchei plain water, and it turned out that Kashchei drank poison from the 10th spring. Before the duel, Ivanushka himself drank poison from any one source and it turned out that he drank the poison with Kashcheev 10, and as a result, this poison was neutralized ..
Correct answer
262. Divide the following number in your mind by two: one sexbillion seven
Paul Sixtillard three and a half
Correct answer
263. How to divide five apples between five people so that one apple remains in the basket? (Joke task)
One in five people must pick up their apple along with the basket. The effect of this not very serious task is based on the ambiguity of the expression "the apple is left lying in the basket." After all, it can be understood both in the sense that no one got it, and in the fact that it simply did not leave the place of its original stay, and these are completely different things. Highlighted in yellow add as a note to the same task, we have it.
Correct answer
264. How can the number 66 be increased by one and a half times without performing any arithmetic operations on it?
The number 66 just needs to be turned upside down. It will turn out to be 99, and this is 66, increased by one and a half times.
Correct answer
265. One lily leaf grows in the pond. The number of leaves doubles every day. On what day will the pond be half-covered with lily leaves if it is known that it will be completely covered with them after 100 days?
The pond will be half covered with lily leaves on day 99. According to the condition, the number of leaves doubles every day, and if on the 99th day the pond is half covered with leaves, then the next day the second half of the pond will be covered with lily leaves, i.e. they will completely cover the pond in 100 days.
Correct answer
266. Is it possible to fly to the Moon by plane? (Keep in mind that airplanes are powered by jet engines, like space rockets, and run on the same fuel as they are.)
The plane in flight "keeps" in the air, so it is impossible to fly to the moon by plane, because there is no air in open space.
Correct answer
267. The girl dropped her ring into a cup containing instant coffee. Why did the ring stay dry?
The water has not yet been poured into the cup.
Correct answer
268. 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 destruction; Two warriors will help you get out - one always speaks the truth, the other always lies, but it is not known which of them is a liar and who is a lover of truth; you can only ask any of them one question. " What question must be asked to get out?
It is necessary to turn to any of the warriors with the following question: "If I ask you, does this exit lead to freedom, then you will answer me yes?" With this formulation of the question, the warrior who lies all the time will be forced to speak the truth. Let's say you, showing him the way out to freedom, say: "If I ask you if this way out leads to freedom, then you will answer me yes?" It will be true in this case if he answers “no”, but he has to lie and therefore he is forced to say “yes”.
Correct answer
269. If three days ago there was a day before Monday, what day will be the day after tomorrow?
Before Monday was Sunday. If three days ago was Sunday, today is Wednesday. If today is Wednesday, then the day after tomorrow will be Friday.
Correct answer
270. The girl was in a taxi. On the way, she chatted so much that the chauffeur became nervous. He told her that he was very sorry, but did not hear a word, because his hearing aid did not work - he was deaf as a cork. The girl fell silent, but when they reached the place, she realized that the driver was playing a trick on her. How did she guess?
If the taxi driver is deaf, how did he know where to take the girl? And one more thing: how did he then understand that she was saying anything at all?
Correct answer
271. You are in the cabin of an anchored ocean liner. At midnight the water was 4 meters below the window and rose half a meter per hour. If this speed doubles every hour, how long does it take for the water to reach the window?
The water never reaches the porthole because the liner rises with the water.
Correct answer
272. A train leaves Moscow for Vladivostok every day. Also, every day a train leaves Vladivostok for Moscow. The move takes 10 days. If you left Vladivostok for Moscow, how many trains going in the opposite direction will you meet during your trip?
At first glance, it may seem that during the trip we will meet ten trains. But this is not so: we will meet not only those ten trains that left Moscow after our departure, but also those that were already on the way by the time of our departure. This means that we will meet not ten, but twenty trains.
Correct answer
273. There is a simple and cheap way to travel, which, surprisingly, no one uses. As you know, the Earth rotates around its axis, and quite quickly (in just 24 hours, each point on the Earth's equator travels approximately 40,000 km - a path equal to the length of the equator). This means that instead of going somewhere by train or flying by plane, or sailing by ship, it is enough for us to rise high above the ground in a balloon or airship and be motionless there for some time. During this time, the Earth will turn towards us with another part of its surface and it will only be necessary to descend to the right place. Is this reasoning correct? If not, what mistake was made in it?
This way of traveling is, of course, unsuitable. The atmosphere, gravitated by the Earth, rotates with it. And even if the atmosphere were motionless, then, having risen into it from the rotating Earth, we would have continued the Earth's motion by inertia for some time. In addition, if the atmosphere were stationary, and the Earth continued to rotate in it (and fast enough: see the condition of the problem), then in this case the most grandiose hurricane would not stop raging on the Earth, which would make impossible not only any travel but also human life itself.
Correct answer
274. Is it possible to boil water on an open flame in a paper box?
The question of the problem, at first glance, seems very strange, because if you hold the paper over the fire, it will surely catch fire. But the point is that the boiling point of water is much lower than the ignition temperature of paper. Since the heat of the flame is absorbed by the boiling water, the paper cannot reach the desired temperature and therefore does not ignite. It is only necessary that the paper is thick enough, otherwise the water will simply tear it and pour out onto the flame. A cardboard box is fine for boiling water. The same explanation underlies the phenomenon of a fireproof piece of paper tightly wound around a metal rod (or steel nail) and embedded in a candle flame. The heat of the fire will be taken up by the rod, preventing the piece of paper from heating up to the desired temperature and catching fire.
Correct answer
275. In one class the pupils were divided into two groups. Some had to always tell only the truth, while others - only the truth. All the students in the class wrote an essay on a free topic, which had to end with the phrase: "Everything written here is true" or "Everything written here is a lie." There were 17 lovers of truth and 18 liars in the class. How many essays came out with a statement about the veracity of what was written?
All lovers of truth correctly asserted that everything they wrote was true, but all liars also falsely claimed that everything they wrote was true. Thus, all 35 essays contained a statement about the veracity of what was written.
Correct answer
276. How many great-great-grandfathers and great-great-grandmothers did you have in total?
Each person has 2 parents, 2 grandmothers and 2 grandfathers, 4 great-grandmothers and 4 great-grandfathers, 8 great-great-grandmothers and 8 great-grandfathers.
Correct answer
277. Dialogue in a hardware store:
How much does one cost?
- 20 rubles, - the seller answered.
How much is 12?
- 40 rubles.
Ok give me 120.
- Please, from you 60 rubles.
What did the visitor buy?
Number for the apartment.
Correct answer
278. A bottle with a cork costs 1 rub. 10 k. A bottle is 1 r. More expensive than a cork. How much does a bottle cost and how much does a cork cost?
At first glance, it may seem that a bottle costs 1 r., And a cork 10 k., But then a bottle is more expensive than a cork by 90 k., And not 1 r., As by condition. In fact, a bottle costs 1 r. 05 k., And the cork costs 5 k.
Correct answer
279. 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 have to go through to get to the second floor?
At first glance, it may seem that Olya goes through 30 steps - two times less than Katya, since she lives two times below her. In fact, this is not the case. When Katya ascends to the fourth floor, she overcomes 3 flights of stairs between floors. This means that there are 20 steps between the two floors: 60: 3 = 20. Olya rises from the first floor to the second, therefore, she overcomes 20 steps.
Correct answer
280. How to pour exactly half of a mug, ladle, saucepan and any other dish of regular cylindrical shape, filled to the brim with water, without using any measuring instruments?
Any dish of regular cylindrical shape, when viewed from the side, is a rectangle. As you know, the diagonal of a rectangle divides it into two equal parts. Likewise, a cylinder is bisected by an ellipse. From a cylindrical dish filled with water, water must be poured until the surface of the water on one side reaches the corner of the dish, where its bottom meets the wall, and on the other side, the edge of the dish through which it is poured. In this case, exactly half of the water will remain in the dishes:
Correct answer
281. Three hens lay three eggs in three days. How many eggs will 12 chickens lay in 12 days?
You can immediately answer that 12 chickens will lay 12 eggs in 12 days. However, it is not. If three hens lay three eggs in three days, then one hen in the same three days lays one egg. Therefore, in 12 days it will lay: 12: 3 = 4 eggs. If there are 12 chickens, then in 12 days they will lay: 12 4 = 48 eggs.
Correct answer
282. Name two numbers in which the number of digits is equal to the number of letters that make up the name of each of these numbers.
One hundred (100) and one million (1,000,000)
Correct answer
283. "I guarantee, - said the seller in the pet store, - that this parrot will repeat any word he heard." The delighted buyer bought the 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? (A joke task.)
The parrot can indeed repeat every word he hears, but he is deaf and does not hear a single word.
Correct answer
284. There is a candle and a kerosene lamp in the room. What will you light first when you enter this room in the evening?
Of course, a match, since without it you cannot light a candle or a kerosene lamp. The question of the problem is ambiguous, because it can be understood either as a choice between a candle and a kerosene lamp, or as a sequence in lighting something (first a match, then everything else from it).
Correct answer
285. Half of half of the number is equal to half. What number is it?
Correct answer
286. Over time, a person will definitely visit Mars. Sasha Ivanov is a person. Consequently, Sasha Ivanov will eventually visit Mars. Is this reasoning correct? If not, what mistake was made in it?
The reasoning is wrong. It is not necessary that Sasha Ivanov will eventually visit Mars. The external correctness of this reasoning is created due to the use of one word in it ("person") in two different senses: in the broad (abstract representative of humanity) and in the narrow (specific, given, this particular person).
Correct answer
287. It is often said that a composer, or an artist, or a writer, or a scientist must be born. Is this true? Is it really necessary to be born a composer (artist, writer, scientist)? (A joke task.)
Of course, a composer, as well as an artist, writer or scientist, must be born, because if a person is not born, then he will not be able to compose music, paint pictures, write novels or make scientific discoveries. This comic task is based on the ambiguity of the question: "Is it really necessary to be born?" This question can be understood literally: is it necessary to be born in order to engage in any kind of activity; and also this question can be understood in a figurative sense: is the talent of a composer (artist, writer, scientist) innate, given by nature, or is it acquired during life by hard work.
Correct answer
288. In order to see, it is not at all necessary to have eyes. Without the right eye, we see. Without the left one, too, we see. And since we have no other eyes apart from the left and right eyes, it turns out that neither eye is necessary for vision. Is this statement true? If not, what mistake was made in it?
The reasoning is, of course, wrong. Its external correctness is based on the almost imperceptible exclusion of one more option, which in this reasoning also had to be considered. This is an option when neither eye can see. It was he who was missed: "Without the right eye, we see, without the left, too, which means that eyes are not necessary for sight." The correct statement should be as follows: “Without the right eye we see, without the left we also see, but without two we do not see together, it means that we see either with one eye, or with the other, or with two together, but we cannot see without eyes, which, thus essential for sight. "
Correct answer
289. The 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?
At first glance, it may seem that a parrot can be asked up to 99 questions. In fact, you can get by with much fewer questions. Let's ask him: "Are you over 50 years old?" If he answers yes, then his age is from 51 to 99 years old; if he answers “no”, then he is from 1 to 50 years old. The number of options for his age after the first question is halved. The next similar question: "Are you over (you may ask - under) 25 years old?", "Are you over (under) 75 years old?" (depending on the answer to the first question) reduces the number of options by four times, etc. As a result, the parrot needs to be asked only 7 questions.
Correct answer
290. 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 twigs in a narrow window. It was possible to crawl into 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 go down. Then I remembered how one wise man lengthened a blanket that was too short for him, cutting off a part of it from the bottom and sewing it on top. So I hastened to split the rope in half and tie the two pieces together again. Then it became long enough, and I safely went down along it. " How did the narrator manage to do this?
The narrator divided the rope not across, as it most likely might seem, but along the length, making two ropes of the same length out of it. When he tied the two pieces together, the rope was twice as long as it was at first.
Correct answer
291. Make a question of five consecutive letters of the Russian alphabet. Hint: it may not be just one word.
Correct answer
292. Before you is an electronic clock. How many times a day will they show the time so that all the cells on the dial (hours, minutes, seconds) are filled with the same number?
Three times: 00.00.00; 11.11.11; 22.22.22
Correct answer
293. A man tossed and turned in bed for a long time at night and could not fall asleep ...
Then he picked up the phone, dialed someone's number, listened to several long beeps - hung up and fell asleep calmly. Question: why could he not fall asleep before?
The truck used up fuel as it got to the center of the bridge.
Correct answer
298. I was invited to a party. There I saw a man with a very rare watch. How do I know this watch was stolen?
Because this watch was mine.
Correct answer
299.8 + 7 = 13 or 7 + 8 = 13?
8 + 7 = 15 and not 13
Correct answer
300. Frau and Herr Myers have 4 daughters. Each daughter has one brother. How many children do the Myers have in total?
5. Four daughters and one son.
Correct answer
The words of Sherlock Holmes: "How many times have I told you, drop everything impossible, then what remains will be the answer, no matter how incredible it may seem," could serve as an epigraph to this chapter.
If solving a puzzle requires only the ability to think logically and does not need to perform arithmetic calculations at all, then such a puzzle is usually called a logical problem. Logic problems, of course, are among the mathematical ones, since logic can be viewed as very general, fundamental mathematics. It is nevertheless convenient to isolate and study logical puzzles separately from their more numerous arithmetic sisters. In this chapter, we will outline three common types of logic problems and try to figure out how to approach their solution.
The most common type of problem that puzzle lovers sometimes call the "Smith - Jones - Robinson problem" (by analogy with the old puzzle invented by G. Dudeny).
It consists of a series of parcels, usually giving some information about the characters; on the basis of these premises, it is required to draw certain conclusions. For example, here is what the latest American version of the Dudeny problem looks like:
1. Smith, Jones and Robinson work in the same train crew as a machinist, conductor and fireman. Their professions are named not necessarily in the same order as their surnames. There are three passengers with the same names on the train, which is served by the crew.
From now on we will respectfully call each passenger "mister" (mr).
2. Mr. Robinson lives in Los Angeles.
3. The conductor lives in Omaha.
4. Mr. Jones has long forgotten all the algebra he was taught in college.
5. The passenger - the conductor's namesake lives in Chicago.
6. The conductor and one of the passengers, a well-known specialist in mathematical physics, go to the same church.
7. Smith always wins against the stoker when he happens to meet for a game of billiards.
What is the name of the driver?
These problems could be translated into the language of mathematical logic, using its standard notation, and seek solutions using appropriate methods, but this approach would be too cumbersome. On the other hand, it is difficult to understand the logical structure of the problem without abbreviations of one kind or another. It is most convenient to use the table, in the empty cells of which we will write all possible combinations of elements of the sets under consideration. In our case, there are two such sets, so we need two tables (Fig. 139).
Rice. 139 Two tables for the problem of Smith, Jones and Robinson.
In each cell we write 1, if the corresponding combination is admissible, or 0, if the combination contradicts the conditions of the problem. Let's see how this is done. Condition 7, obviously, excludes the possibility that Smith is a fireman, so we write 0 in the cell in the upper right corner of the left table. Condition 2 tells us that Robinson lives in Los Angeles, so we write in the lower left corner of the table 1, and all other cells in the bottom row and left column are 0 to indicate that Mr. Robinson does not live in Omaha or Chicago, and Mr. Smith and Mr. Jones do not live in Los Angeles.
Now we have to think a little. From conditions 3 and 6 it is known that a mathematical physicist lives in Omaha, but we do not know his last name. He cannot be neither Mr. Robinson, nor Mr. Jones (after all, he forgot even elementary algebra).
Therefore, it must be Mr. Smith. We note this circumstance by placing 1 in the middle cell of the upper row of the right table and 0 in the remaining cells of the same row and empty cells in the middle column. The third unit can now be inscribed in only one cell: this proves that Mr. Jones lives in Chicago. From condition 5, we learn that the conductor also has the surname Jones, and we enter 1 in the central cell of the left table and 0 in all the other cells in the middle row and middle column. After that, our tables take the form shown in Fig. 140.
Rice. 140 Table The eggs shown in Fig. 139, after pre-filling.
Now it is no longer difficult to continue the reasoning leading to the final answer. In the column with the inscription "Fireman", the unit can only be placed in the lower cell. It immediately follows that in the lower left corner should be 0. Only the cell in the upper left corner of the table remains empty, where you can put only 1. So, the driver's surname is Smith.
Lewis Carroll was fond of inventing extremely complex and cunning problems of this kind. John J. Kemeny, the dean of the mathematics department at Dortmouth College, programmed one of the monstrous (with 13 variables and 12 conditions, from which it follows that "no judge sniffs tobacco") Carroll problems for the IBM-704 computer. The machine coped with the solution in about 4 minutes, although it would take 13 hours to print the complete "truth table" of the problem (a table showing whether the possible combinations of truth values of the problem variables are true or false)!
For readers who want to try their luck at solving a problem that is more difficult than the Smith-Jones-Robinson problem, we offer a new puzzle. Its author is R. Smullian of Princeton University.
1. In 1918 the First World War ended. On the day of the signing of the peace treaty, three married couples gathered to celebrate the event at a festive table.
2. Each husband was the brother of one of the wives, and each wife was the sister of one of the husbands, that is, among those present one could indicate three related pairs "brother and sister."
3. Helen is exactly 26 weeks older than her husband, who was born in August.
4. Mr. White's sister is married to Brother Helen's brother-in-law and married him on her birthday in January.
5. Margaret White is shorter than William Blake.
6. Arthur's sister is prettier than Beatrice.
7. John is 50 years old.
What's Mrs Brown's name?
Another type of logical problems is no less widespread, which, by analogy with the following well-known example, can be called problems of the "problem of colored caps" type. Three people (let's call them A, B and WITH) are blindfolded and said that each of them had either a red or a green cap on their heads. Then they are untied their eyes and asked to raise their hand if they see a red cap, and leave the room if they are sure that they know what color the cap is on their head. All three caps turned out to be red, so all three raised their hand. Several minutes passed and WITH who is more clever than A and V, left the room. How WITH was able to establish what color the cap is on it?
[The problem of the wise men in green caps is formulated in the text in such a way that it cannot have a solution. This is especially evident when the number of sages is large. How long does it take for the first wise man to guess the true situation?
At the end of the forties, this problem was intensively discussed in Moscow in school mathematics circles, and a new version of it was invented, in which discrete time was introduced. This task looked like this.
In ancient times, sages lived in the same city. Each of them had a wife. In the morning they came to the bazaar and found out all the city gossip there. They were gossips themselves. It gave them great pleasure to learn about the infidelity of any of the wives - they knew about it immediately. However, one unspoken rule was strictly observed: the husband was never informed about his wife, since each of them, having learned about their own shame, would have kicked their wife out of the house. So they lived, enjoying intimate conversations and remaining completely unaware of their own affairs.
But one day a real gossip came to town. He came to the market and publicly declared: "But not all wise men have faithful wives!" It would seem that the gossip had not said anything new - and so everyone knew it, every sage knew it too (only with malice he thought not of himself, but of something else), so none of the inhabitants paid attention to the words of the gossip. But the sages began to think - that's what they are sages - and on n the day after the arrival of the gossip, the sages drove out the unfaithful wives (if there were n).
The reasoning of the sages is not difficult to restore. It is more difficult to answer the question: what information did the gossip add to the one that was known to the sages without him?
This problem has been repeatedly encountered in the literature].
S asks himself if his cap could be green. If this were the case, then A would immediately have known that he was wearing a red cap, because only a red cap on his head could make V raise a hand. But then A would leave the room. V would think in exactly the same way and also leave the room. Since neither one nor the other came out, WITH concluded that his own cap should be red.
This problem can be generalized to the case when there are any number of people and all of them are wearing red caps. Suppose there is a fourth character in the problem D, even more discerning than C. D could reason like this: “If my cap were green, then A, B and WITH would find themselves in exactly the same situation as just described, and in a few minutes the smartest of the trio would certainly leave the room.
But five minutes have passed, and none of them come out, therefore, my cap is red. "
If a fifth participant appeared, even smarter than D, then he could come to the conclusion that he was wearing a red cap after waiting ten minutes. Of course, our reasoning loses its credibility due to assumptions about varying degrees of intelligence. A, B, C... and rather vague considerations as to how long the most ingenious person should wait before he can confidently name the color of his cap.
Some other colored cap problems contain less ambiguity. Such, for example, is the following problem, also invented by Smullian. Each of the three - A, B and WITH- is fluent in logic, that is, he is able to instantly extract all the consequences from a given set of premises and knows that others also have this ability.
We take four red and four green stamps, blindfold our "logicians" and stick two stamps on each of them on the forehead. Then we remove the blindfolds from their eyes and, in turn, set A, B and WITH the same question: "Do you know what color the stamp is on your forehead?" Each of them replies in the negative. Then we ask again A and again we get a negative answer. But when we ask the same question a second time V, he answers in the affirmative.
What color are the marks on the forehead V?
The third type of popular logic puzzles is the problem of liars and those who always tell the truth. In the classical version of the problem, we are talking about a traveler who found himself in a country inhabited by two tribes. Members of one tribe always lie, members of another tell only the truth. The traveler meets two natives. "Do you always tell only the truth?" he asks the tall native. He answers: "Tarabara". "He said yes," explains the smaller native who knows English, "but he's a terrible liar." Which tribe does each of the natives belong to?
A systematic approach to the solution would consist in writing out all four possibilities: AI, IL, LI, LL (I means “true”, L- “false”) - and excluding those from them that contradict the given problem. The answer can be obtained much more quickly if you notice that the tall native must answer in the affirmative, regardless of whether he is lying or telling the truth. Since the smaller native told the truth, he must belong to the tribe of the truthful, and his tall friend - to the tribe of liars.
The most famous problem of this type, complicated by the introduction of probabilistic weights and not a very clear formulation, can be found rather unexpectedly in the middle of the sixth chapter of the book by the English astronomer A. Eddington "New Pathways in Science". "If A, B, C and D tell the truth in one out of three cases (independently of each other) and A States that V denies that WITH says like D liar, then what is the probability that D told the truth? "
Eddington's response, 25/71, was greeted with a barrage of protests from readers and sparked a funny and confusing controversy that was never resolved. The English astronomer G. Dingle, the author of a review of Eddington's book, published in the journal Nature (March 1935), believed that the problem did not deserve attention at all as meaningless and only testified that Eddington had not sufficiently thought out the basic ideas of the theory of probability. The American physicist T. Stern (Nature, June 1935) objected to this, stating that, in his opinion, the problem was by no means meaningless, but the data were insufficient to solve it.
In response, Dingle noted (Nature, September 1935) that if we take Stern's point of view, then there is enough data for a solution and the answer will be 1/3. Eddington then got into the fray, publishing (Mathemetical Gazette, October 1935) an article detailing how he got his answer. The controversy culminated in two more articles appearing in the same journal, one of which defended Eddington, while the other advanced a different point of view.
The difficulty lies mainly in understanding Eddington's formulation. If V, expressing his denial, is telling the truth, then can we reasonably assume that WITH said that D spoke the truth? Eddington believed that there was insufficient basis for such an assumption. Likewise if A lies, then can we be sure that V and WITH did you say anything at all? Fortunately, we can get around all these language difficulties by making the following assumptions (Eddington did not):
1. None of the four remained silent.
2. Statements A, B and WITH(each of them separately) either confirm or deny the following statement.
3. A false statement coincides with its negation, and a false negation coincides with a statement.
All four of them lie independently of each other with a probability of 1/3, that is, on average, any two of their three statements are false. If a true statement is denoted by the letter AND, and false - with the letter L then for A, B, C and D we get a table of eighty-one different combinations. From this number, one should exclude those combinations that are impossible due to the conditions of the problem.
Number of allowed combinations ending with a letter AND(that is, a truthful - true - statement D), should be divided by the total number of all valid combinations, which will give the answer.
The formulation of the problem of a traveler and two natives should be clarified. The traveler realized that the word "gibberish" in the language of the natives means either "yes" or "no", but he could not guess what exactly. This would allow warning several letters, one of which I quote below.
The tall native, apparently, did not understand a word of what the traveler said (in English) to him, and could not answer "yes" or "no" in English. So his "gibberish" means something like "I don't understand" or "Welcome to Bongo Bongo." Consequently, the little native lied, saying that his friend had answered "yes," and since the little one was a liar, he also lied when he called the tall native a liar. Therefore, the tall native must be considered truthful.
So the feminine logic has dealt a blow to my masculine vanity. Doesn't it hurt your author's pride a little too?
Answers
The first logical problem is best solved using three tables: one for combinations of first and last names of wives, the second for first and last names of husbands, and the third for family ties.
Since Mrs. White's name is Margaret (condition 5), we have only two options for the names of the other two wives: a) Helen Blake and Beatrice Brown, or b) Helen Brown and Beatrice Blake.
Let us assume that the second of the possibilities takes place. White's sister should be either Helen or Beatrice. But Beatrice cannot be Wayne's sister, because then Helen's brother would be Blake, and Blake's two brothers-in-law would be White (his wife's brother) and Brown (his sister's husband); Beatrice Blake is not married to any of them, which contradicts condition 4. Therefore, Helen must be White's sister. From this, in turn, we conclude that Brown's sister's name is Beatrice, and Blake's sister's name is Margaret.
Condition 6 implies that Mr. White's name is Arthur (Brown cannot be Arthur, since such a combination would mean that Beatrice is more beautiful than herself, and Blake cannot be Arthur, since from condition 5 we know his name: William). So, Mr. Brown can only be John. Unfortunately, from condition 7 we see that John was born in 1868 (50 years before the signing of the peace treaty). But 1868 is a leap year, so Helen must be one day older than her husband than the 26 weeks mentioned in condition 3. (From condition 4 we know that she was born in January, and from condition 3 that her husband was born in August. She could be exactly 26 weeks older than her husband if her birthday was on January 31, and his - on August 1, and if there were no February 29 between these dates!) So, the second of the possibilities, with which we started out should be dropped, which allows us to name the wives: Margaret White, Ellen Blake, and Beatrice Brown. There is no contradiction here, since we do not know Blake's year of birth. From the conditions of the problem, we can conclude that Margaret is Brown's sister, Beatrice is Blake's sister, and Helen is White's sister, but the question of the names of White and Brown remains unresolved.
In the problem with stamps, V there are three possibilities. His marks can be: 1) both red; 2) both are green; 3) one is green and the other is red. Suppose both stamps are red.
After all three have answered once, A can reason like this: “The marks on my forehead cannot be both red (because then WITH would see four red marks and would immediately know that he had two green marks on his forehead, and if WITH both stamps were green, then V if he saw four green marks, he would have realized that he had two red marks on his forehead). Therefore, I have one green and one red stamp on my forehead. "
But when A asked a second time, he did not know what color his brand was. It allowed V discard the possibility that both of his own stamps are red. Reasoning exactly the same as A, B ruled out the case when both of his brands are green. Consequently, he was left with the only option: one stamp is green, the other is red.
Several readers quickly noticed that a problem can be solved very quickly without going into question and answer analysis. Here is what one of the readers wrote about this: “The conditions of the problem are completely symmetric with respect to the red and green stamps.
Therefore, distributing marks between A, B and WITH observing all the conditions of the problem and replacing red marks with green ones and, conversely, green ones with red ones, we will arrive at a different distribution, for which all conditions will also be fulfilled. It follows that if the solution is unique, then it should be invariant (should not change) when replacing green marks with red ones, and red ones with green ones. Such a solution can only be such a distribution of stamps, in which B will have one green and one red stamp ”.
As the Dean of the Department of Mathematics at Brooklyn College W. Manheimer put it, this elegant solution comes from the fact that they are not fluent in logic. A, B and WITH(as stated in the problem statement), and Raymond Smullian!
In Eddington's problem, the probability that D tells the truth, is 13/41. All combinations of truth and falsehood that contain an odd number of times false (or true) should be discarded as contradicting the conditions of the problem. As a result, the number of possible combinations decreases from 81 to 41, of which only 13 end with a truthful statement. D... Insofar as A, B and WITH tell the truth in cases that correspond to exactly the same number of allowable combinations, the probability of telling the truth is the same for all four.
Using the equivalence symbol
meaning that the statements connected by him are either both true or both are false (then the false statement is true, otherwise it is false), and the negation symbol ~, Eddington's problem in the language of the propositional calculus can be written as follows:
or after some simplifications like this:
The truth table of this expression confirms the answer already received.
Notes:
Then frustrate- upset, do something in vain, hopeless, doom to failure (English).
See the chapter on Raymond Smullian in the book M. Gardner Time Travel (Moscow: Mir, 1990).
Eddington a... New Pathways in Science. - Cambridge: 1935; Michigan: 1959.
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