Tasks for logical thinking. Logic problems

Let's stretch our brains! This article contains logical and mathematical problems that are often encountered in interviews and may come across to you.

The main problems that often arise during the interview process are not lack of experience or training. Even a truly experienced developer can easily stumble while solving some cleverly tailored problem. Therefore, we will not talk about how to write a resume and present yourself favorably. We focus on solving non-trivial problems that involve logical and/or mathematical solutions.

"Toughie"

Remember the riddle from the third film? If not, then remember, because they like to regale this question at Microsoft.

Task:

There are 2 empty buckets: the first is 5 liters, the second is 3 liters. How can you use them to measure 4 liters of water?

First, fill a five-liter bucket. Next, pour water from it into a three-liter bottle so that 2 liters of water remain in the five-liter bottle (completely filling the three-liter bottle). Empty all the water from the smaller bucket and pour the remaining 2 liters into it. Fill the five-liter bucket again and pour one liter into the three-liter bucket (it will just fill): this will leave 4 liters of water in the larger bucket.

Jars of pills

Task:

There are twenty bottles of pills. In almost all of them, the tablets weigh 1 g, and only in one - 1.1 g. We have precise scales with which we need to determine the jar, each tablet of which weighs 1.1 g. How to do this if you can only weigh 1 time?

Let's abstract ourselves and imagine that we have 2 jars, one of which contains heavier tablets. Even if we put both of them on the scale, we won't know anything. But if we take 1 tablet from one jar, 2 from another and put them on the scales, then the truth will be revealed :) In this case, the weight will be 2.1 or 2.2 (depending on how many tablets we have have taken). This is how we define our jar.

Let's return to the task. You need to remove a different number of tablets from each jar. That is, from the first jar there is 1 tablet, from the second - 2, from the third - 3, and so on. If each tablet weighed 1 g, the total weight would be 210 g. But since the tablets in one of the jars are heavier, the weight will be greater. To determine the required jar, we simply use the formula:

No. of heavy jar = (weight - 210) * 10

But the interesting logic doesn’t end there. Go ahead!

Date

Task:

The guy and the girl agreed to meet exactly at 21:00. The problem is that both their clocks are wrong. The girl's watch is 2 minutes fast, but she thinks it is 3 minutes fast. behind. The guy’s watch is 3 minutes behind, but he thinks it’s 2 minutes behind. in a hurry. Which of the couple will be late for the date?

Nothing complicated: pure mathematics. If a girl’s watch is rushing, and she thinks that it is behind, she will hurry up and come in 5 minutes. earlier. The guy, on the contrary, will consider that he still has 5 minutes of time left, which is why for these same 5 minutes. will be late.

Calculating the weight of the chicken

Task:

The length of a chicken when measured from head to tail will be 45 cm, but from tail to head (if measured along the belly) - 53 cm. According to statistics, the density of a chicken per unit of lateral projection is 8 g/cm 2 . The average height of a chicken, if measured along the side surface, is 21 cm. How much does a kilogram of chicken weigh?

A kilogram of chicken weighs 1 kilogram.

Yes, there are tricky math problems too :)

Book pages

Task:

The book contains N pages, which are numbered in the standard way: from 1 to N. If you add up the number of digits (not the numbers themselves) that are contained in each page number, you get 1095. So how many pages are there in the book?

Total 401 pages.

Each page number has a 1 digit, so there are N 1 digits. But after 9, two-digit numbers begin, and we need to add N-9 digits. The same with three-digit numbers that start after 99: add N-99 digits. There is no point in continuing, since the amount does not imply more than 999 pages. We get the following formula:

Mathematical problems in interviews can be quite simple, but often only at first glance. Try dividing 30 by 1/2 in your head and adding 10. What will be the result?

The first solution that usually comes to mind is wrong:

If we divide by a fraction, we need to turn it over and multiply:

Digit 3

Task:

How many integers in the range 1-1000 contain the number 3? You cannot use a computer when counting.

And there is also a group of numbers (100 of them) that end in three: 2-993. We exclude from it such 10 numbers as 303, 313 ... 393 (they were taken into account earlier). We get another +90 numbers. 1/10 of these 90 also have a three in place of a ten: 33, 133 ... 933. We remove another 9, leaving 81 numbers. The following is simple math:

100 + 90 + 81 = 271

Here's a more elegant solution to this problem. First, we count how many numbers do not include a triple (9 digits that are not triples are placed in each of the 3 places):

1000 - 729 = 271

Remember that we need to take into account simply the fact that the number contains three. If, for example, it is 33, we do not count the number 2 times. There must be at least one three in the number to count. For example, numbers in the range 300-399 give us 100 numbers at once. We get another 10 from 30-39. The same applies to 130-139, 230-239, etc. A dozen of these numbers were already taken into account when calculating 330-339, so we remove it and get:

And there is also a group of numbers (100 of them) that end in three: 2-993. We exclude from it such 10 numbers as 303, 313 ... 393 (they were taken into account earlier). We get another +90 numbers. 1/10 of these 90 also have a three in place of a ten: 33, 133 ... 933. We remove another 9, leaving 81 numbers. The rest is simple math.

Preschoolers solve this problem in 5-10 minutes. Some programmers take up to an hour to complete it. But many people, after writing several sheets of paper, give up.

Parking space number

It usually takes a six-year-old child no more than 20 seconds to solve this problem. But it often confuses unprepared adults. So what number is hidden under the car?

Riddle for a genius

A genius finds a solution in 10 seconds. Bill Gates - in 20 seconds. Harvard University graduate - in 40 seconds. If you found the answer in 2 minutes, then you belong to the 15% of most gifted people. 75% of people are unable to solve this problem.

Ruler of the Island

The autocratic ruler of one island wanted to prevent aliens from settling on the island. Wanting to maintain the appearance of justice, he issued an order according to which anyone wishing to settle on the island must, after thinking carefully, make any statement, and after a preliminary warning that his life depended on the content of this statement. The order read: “If the alien tells the truth, he will be shot. If he tells a lie, he will be hanged." Can an alien become an island resident?

Project approval

According to the agreement, the procedure for approving a new project in the development of which institutions A, B, and C participate is as follows: if A and B participate in the approval first, then institution B must also participate. If approval occurs first in institutions B and C, Institution A also joins. The question is: are such cases possible when approving a project when only institutions A and B would take part in it, while the participation of institution B would not be necessary (while maintaining the agreement on the procedure for approving projects)?

Two tribes

There are two tribes living on the island: well done. Those who always tell the truth, and liars who always lie. The traveler met the islander, asked him who he was, and when he heard that he was from a tribe of fellows, he hired him as a guide. They went and saw another islander in the distance, and the traveler sent his guide to ask him to what tribe he belonged. The guide returned and said that he claimed to be from a tribe of fellows. The question is: was the guide a good guy or a liar?

Aborigines and Aliens

Three people stand before the court, each of whom can be either an aborigine or an alien. The judge knows that natives always answer questions truthfully, but aliens always lie. However, the judge does not know which of them is a native and which is an alien. He asks the first one, but does not understand his answer. Therefore, he asks first the second, and then the third, what the first answered. The second one says that the first one said he was an Aborigine. The third says that the first called himself an alien. Who were the second and third defendants?

Beetle on tape

The beetle went on a journey. He crawls along a tape, the length of which is 90 centimeters. At the other end of the ribbon, two centimeters from the end, is a flower. How many centimeters will the beetle have to crawl to the flower: 88 or 92 (provided that it crawls all the time on one side and only at the end can it cross the end of the tape to the other side)?

Purchase

Marina spent a long time choosing which jug to buy. Finally I chose. The saleswoman put the purchase in a box. What did Marina buy? How many jugs did the saleswoman put on the shelves, which ones they were on before?

Tourist

The tourist was walking towards the lake. He reached a crossroads, from where one road led to the right and the other to the left; one went to the lake, the other did not. There were two guys sitting at a crossroads, one of them always told the truth, the other always lied. Both of them answered either “yes” or “no” to any question. The tourist knew all this, but he did not know which of them was telling the truth and which was lying; he also did not know which road led to the lake. The tourist asked only one question to one of the guys. What kind of question was it, since he knew from the answer which road led to the lake?

broken window

During the break there were nine students left in the class. One of them broke the window. The following answers were received to the teacher's question:

How many triangles?

What team?

Read carefully and do not write anything down: Torpedo tops the standings, Spartak is in fifth place, and Dynamo is right in the middle between them. If Lokomotiv is ahead of Spartak, and Zenit takes place immediately behind Dynamo, then which of the listed teams is in second place? You are given 30 seconds to think.

Project approval procedure

The enterprise has three workshops - A, B, C, which have agreed on the procedure for approving projects, namely: 1. If workshop B does not participate in the approval of the project, then workshop A does not participate in this approval. 2. If workshop B takes part in approval of the project, then workshops A and C take part in it. The question is: under these conditions, is workshop C obliged to take part in the approval of the project when workshop A takes part in the approval?

An evening walk

Which of these nine mustaches went for an “evening walk”?

7 buttons

Which of the 7 buttons should you press? For the bell to ring? It is recommended to find the path mentally.

Make a table

In the Moscow semi-final of the European Basketball Championship, held in Soviet times, the places were distributed as follows: USSR - 14 points, Italy and Czechoslovakia - 12 each, Israel - 11, Finland - 10, East Germany and Romania - 9 each and Hungary - 7 points. According to the regulations. Each team received 2 points for a win, 1 point for a loss, and 0 points for a no-show. No draws were allowed. Make a summary table of the results of the games if you know that the Finnish team won against the Italian team and lost to the Romanian team.

On Tuesday at about 10 o'clock in the morning a stranger burst into Inspector Warnicke's room. He was extremely excited. His hands were shaking, his tousled hair stuck out in all directions. A few minutes later, having lit a cigarette and calmed down, the visitor began his story: - This morning I returned from vacation. I had to shake on the train all night. I didn’t get enough sleep and, when I came home, I decided to lie down on the sofa. Because of fatigue, I did not immediately notice that the piano had disappeared from the room, and the coffee table and armchair had been moved out of place. On this piece of paper I drew a plan for the arrangement of furniture in the room before I left. “Here’s what, dear,” said Inspector Warnicke, quickly glancing at the drawing, “First of all, it’s absolutely clear to me that you didn’t have a piano at all.” Now let's find out why you needed this lie. Why did Inspector Warnicke doubt the veracity of the visitor's story?

LOGIC PROBLEMS

Logical problems, just like mathematics, are called “mental gymnastics.” But, unlike mathematics, logic problems is an entertaining gymnastics that allows you to test and train your thought processes in a fun way, sometimes from an unexpected perspective. Solving them requires intelligence, sometimes intuition, but not special knowledge. Solving logic problems consists in thoroughly analyzing the conditions of the problem, unraveling the tangle of contradictory connections between characters or objects. Logic problems for children- these are, as a rule, whole stories with popular characters, which you just need to get used to, feel the situation, visually imagine it and catch the connections.

Even the most difficult logic problems do not contain numbers, vectors, functions. But a mathematical way of thinking is necessary here: the main thing is to comprehend and understand the condition logical problem. The most obvious solution on the surface is not always the right one. But most often, solving a logic problem turns out to be much simpler 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 increased interest in these academic disciplines and help in their meaningful study. Logic problems on weighing, transfusion, tasks on non-standard logical thinking will help in everyday life to solve everyday problems in a non-standard way.

In the process of solving logic problems 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 patterns of reasoning, which he called syllogisms. One of his most famous syllogisms is: “Socrates is a man; all people are mortal; So Socrates is mortal." Logic (from ancient Greek. Λογική - speech, reasoning, thought) is the science of correct thinking, or, in other words, the “art of reasoning.”

There are certain techniques solving logical problems:

a way of reasoning with which the simplest logical problems are solved. This method is considered the most trivial. During 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.

table method used in solving text logic problems. As the name suggests, solving logical problems involves constructing tables that allow you to visualize the conditions of the problem, control the reasoning process, and help you draw correct logical conclusions.

The method of graphs is to enumerate possible options for the development of events and ultimately select the only correct solution.

The flowchart method is 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 flowchart, which is essentially a program, the execution of which leads to the solution of the task.

The billiards method follows from trajectory theory (one of the branches of probability theory). To solve the problem, you need 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 used in solving logic problems for grades 1, 2, 3, 4, 5, 6, 7, 8, 9.

We present you a wide variety logic problems for grades 1, 2, 3, 4, 5, 6, 7, 8, 9. We have selected for you the most interesting logic problems with answers, which will be of interest not only to children, but also to parents.

• choose for the child logic problems in accordance with his age and development
• take your time to reveal the answer, let the child find it himself logical solution tasks. Let him come to the correct decision himself and you will see what pleasure and feeling of delight he will have when his answer coincides with the given one.
• in progress solving logic problems Leading questions and indirect clues indicating the direction of reflection are acceptable.

Using our selection logic problems with answers you will really learn to solve logical problems, expand your horizons and significantly develop logical thinking. Go for it!!!

Solving logical problems - the first step towards child development.

E. Davydova

Logic is the art of arriving to an unpredictable conclusion.

Samuel Johnson

Without logic it is almost impossible to enter our world brilliant discoveries of intuition.

Kirill Fandeev

A person who thinks logically stands out nicely against the backdrop of the real world.

American saying

Logic is the morality of thought and speech.

Jan Lukasiewicz

In this section you are presented with many logical problems or logic problems. You can pre-hide the answers by clicking on the appropriate button below (HIDE ANSWERS). To see the answer to the problem, you must click on the word “Answer” located below. Solving logical problems makes the brain think and trains logic, memory, and thinking.

The problems in this section are designed for different age groups and are suitable for solving: adults, students, teenagers, schoolchildren, children.

A logic task is a task the solution of which, as a rule, requires logical thinking, ingenuity, and sometimes the use of non-standard thinking, and not high-level special knowledge. Therefore, its solution will help you both test and improve your intelligence and logical thinking.

In a forest health center in a clearing, two athletes are playing table tennis. After another strong hit with the racket, the tennis ball flew far away and rolled into a steel pipe, vertically dug deep (several meters) into the ground. The ball ended up at the very bottom of the pipe (several meters from the surface of the earth). For the athletes, this was the only ball. Please tell me how they can pull out a tennis ball without much effort, without having to dig up such a long pipe?

Answer

What do you think your friends and acquaintances use more often than you, but it is your property?

Answer

If you have this, then you have the full part. If you share this with someone, will it disappear completely?

Answer

Until it is measured, it is not known. However, if it constantly flies, then many people often do not like it. What is this?

Answer

Imagine that in your sock closet you have: 4 white socks, 8 black socks, 3 brown socks and 5 gray socks. What is the minimum number of socks you need to pull out of your closet without looking at it to be sure that you get at least one pair of identical socks?

Answer

If you call her name, it will immediately disappear. What it is?

Answer

You saw him where he had never been and could not be. But you see him there very often. Who is he and where could he not be, but do you see him there often?

Answer

Continue with the following sequence of letters:

What constantly walks, but most of the time staying in one place?

Answer

Do you think that if a woman is cold as a fish, then a man should be patient like...?

Answer

You need to find out the pattern by which the numbers appear in this sequence and indicate the number that should continue this sequence:

Alexander has his own pet store selling birds. If he puts one bird in each cage, then one bird is not enough for the cage. If Alexander places two birds in each cage, then one cage will remain free. How many cages and birds do you think are in Alexander's pet store?

Answer

Alexander weighs half as much as Dmitry, and Nikolai weighs 3 times more than Alexander. Try to determine how much each of them weighs, if all together they weigh 360 kilograms?

Answer

If Jack doesn't drink at work, then for some reason all his employees begin to think that he is a bad worker and a slacker. Why do you think?

Training logical thinking (for children 5-7 years old)

Find a pattern and match the word.

Bird - feathers. Fish - ... (scales)
Cucumber is a vegetable. Chamomile -...
Teacher - school. Doctor -...
Table - tablecloth. Floor -...
Morning - breakfast. Evening -...
Man - hands. Cat -...
Fish-water. Bird -...
Red - stand. Green - ...
Autumn - rain. Winter -...

Who is this? What is this? Guess who or what is being talked about.

Green, long, juicy. (cucumber)
Brown, clubfooted, clumsy. (bear)
Cold, white, fluffy. (snow)
New, interesting, library. (book)
Small, gray, shy. (mouse)
White-trunked, tall, slender. (birch)

Choose words that have opposite meanings.

Black White.
Big -...
Funny -...
Wide -...
High -...
Kind -...
Cold -...
Good -...
Thick -...
Solid -...
Smart -...
Fast -...
Healthy -...
Bitter -...

Choose words that have opposite meanings:

Day Night.
Winter - ...
North -...
Cold - ...
A lot of - ...
Start - ...
First - ...
Welcome -...
Joy - ...
Far - ...

Answer the questions. Name different professions.

Who cooks dinner?
Who builds houses?
Who writes poetry?
Who sings the songs?
Who treats children?
Who sews the clothes?
Who paints the pictures?
Who paints the walls?
Who flies into space?
Who drives the car?

Think and solve logical problems.

1) Which is heavier: a kilogram of cotton wool or a kilogram of iron?
2) Which lasts longer: a year or 12 months?
3) Marina and Tanya drank different juices - grape and apple. Marina did not drink apple juice. What juice did Tanya drink?
4) Kostya and Artem were wearing jackets of different colors: blue and green. Kostya was not wearing a blue jacket. What color jacket was Artem wearing?

Think and solve logical problems. Explain your answers.

1) Who will swim to the shore faster - ducklings or chickens?
2) Who will reach the flower faster - a butterfly or a caterpillar?
3) Mom has a cat Fluff, a daughter Dasha and a dog Sharik. How many children does mom have?
4) Four eggs are boiled for four minutes. How many minutes does it take to cook one egg?
5) Who will moo louder, a rooster or a cow?
6) How many mushrooms can be grown from spruce seeds?
7) Three sparrows sat on the water, one flew away. How much is left?
8) What is the best and fastest way to pick a watermelon from a tree?

Listen to the stories and answer the questions.

1) Vova woke up in the morning, ran to the window and exclaimed in surprise: “Mom, it was raining outside at night!” How did Vova guess that it was raining, since he was fast asleep at that time?
2) Looking out the window, Vera said to her mother: “Mom, you need to dress warmly, there is such a strong wind outside!” How did Vera guess that there was a strong wind outside?
3) An ant descends from the mountain, and a donkey meets it. The donkey asks the ant: “Please tell me, ant, what kind of grass is on the mountain?” “So tall and thick,” answered the ant. The donkey was happy and climbed the mountain, but no matter how hard he tried to pinch the grass with his lips, he just couldn’t. “The ant deceived me,” thought the donkey. What do you think, did the ant deceive the donkey?
4) The cat Vaska and his owner are sitting in a boat. The owner casts a fishing rod and says:
-Catch, big, big fish!
And Vaska quietly mutters:
- Little catch, little one!
Why does he say that?

Think and solve problems.

1) Nastya had 4 ribbons. She cut one of them into two equal parts. How many ribbons does Nastya have?
2) Geese were walking around the yard. Sasha counted 6 paws on all the geese. How many geese were walking in the yard?
3) Several birds were sitting on a branch. They only have 8 wings. How many birds were sitting on the branch?
4) Two friends played chess for 3 hours. How long did each of them play?

Read funny poems.

All kids need to know:
Two plus two, of course... (five?)

Everyone in the whole world knows:
Fingers on the hand... (four?)

All the guys know for sure:
Cats are very loud...(barking?)

Our kitten gallops deftly,
He really loves...(carrots?)

Our Seryozha is very smart,
He always laughs...(sad?)

They took the cat's fish,
Should he say... (thank you?)

There is a rich house and a poor one. They are burning. Which house will the police extinguish?

Police don't put out fires, firefighters put out fires

How can a person not sleep for 8 days?

Sleep at night

You enter a dark kitchen. It contains a candle, a kerosene lamp and a gas stove. What will you light first?

A girl is sitting, and you cannot sit in her place, even if she gets up and leaves. Where is she sitting?

She sits on your lap

You are standing in front of three switches. Behind an opaque wall are three light bulbs that are turned off. You need to manipulate the switches, go into the room and determine which light bulb each switch belongs to.

First you need to turn on two switches. After some time, turn off one of them. Enter the room. One light bulb will be hot from the switch on, the second will be warm from the switch off, the third will be cold from the untouched switch.

It is known that among the nine coins there is one counterfeit one, which weighs less than the rest of the coins. How can you identify a counterfeit coin in two weighings using a cup scale?

1st weighing: 3 and 3 coins. The counterfeit coin is in the pile that weighs less. If they are equal, then the fake is in the third pile. 2nd weighing: Any 2 coins from the pile with the lowest weight are compared. If they are equal, then the remaining coin is fake

Two people approach the river. There is a boat at the shore that can only support one. Both people crossed to the opposite bank. How?

They were on different banks

Two fathers, two sons found three oranges and divided them. Everyone got a whole orange. How can this be?

The dog was tied to a ten-meter rope and walked 300 meters. How did she do it?

The rope was not tied to anything

How can a thrown egg fly three meters without breaking?

You need to throw the egg four meters, then the first three meters it will fly intact

The man was driving a large truck. The lights on the car were not turned 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

If five cats catch five mice in five minutes, how long does it take one cat to catch one mouse?

Five minutes

Is it possible to light a match underwater?

It is possible if you pour water into some container, for example, into a glass, and hold the match below the glass

The boat rocks on the water. A ladder was thrown from it along the side. Before high tide, the water covered only the bottom step. How long will it take for the water to cover the 3rd step from the bottom if during high tide the water rises at 20 cm per hour and the distance between the steps is 30 cm?

Never, because the boat rises with the water

How to divide five apples between five girls so that each gets an apple and at the same time one of the apples remains in the basket?

Give one girl an apple along with a basket

One and a half pike perch costs one and a half rubles. How much do 13 pike perch cost?

Traders and potters. In one city all the people were traders or potters. Merchants always told lies, but potters always told the truth. When all the people gathered in the square, each of those gathered said to the others: “You are all traders!” How many potters were there in this city?

The potter was alone because:

If there were no potters, then the traders would have to tell the truth that all the other traders are traders, and this contradicts the conditions of the problem.

If there were more than one potter, then each potter would have to lie that the rest were traders.

There are two coins on the table; they add up to 3 rubles. One of them is not 1 ruble. What coins are these?

1 and 2 rubles

The satellite makes one revolution around the Earth in 1 hour 40 minutes, and the other in 100 minutes. How can it be?

100 minutes is 1 hour 40 minutes

As you know, all Russian female names end with either the letter “a” or the letter “ya”: Anna, Maria, Irina, Natalya, Olga, etc. However, there is only one female name that ends with a different letter. Name it.

What has no length, depth, width, height, but can be measured?

Time, temperature

If it rains at 12 o'clock at night, can we expect sunny weather 72 hours later?

No, because in 72 hours it will be night

Seven brothers have one sister. How many sisters are there in total?

One yacht goes from Nice to Sanremo, the other from Sanremo to Nice. They left the harbors at the same time. For the first hour, the yachts moved at the same speed (60 km/h), but then the first yacht increased its speed to 80 km/h. Which yacht will be closer to Nice when they meet?

At the moment of their meeting they will be at the same distance from Nice

A woman was walking towards Moscow, and three men met her. Everyone has a bag, in each bag there is a cat. How many creatures were heading to Moscow?

Only the woman went to Moscow, the rest went in the other direction

There were 10 birds sitting on a tree. A hunter came and shot one bird. How many birds are left on the tree?

Not a single one - the rest of the birds flew away

The train runs from east to west, and the wind blows from north to south. In which direction does the smoke fly from the chimney?

You are running a marathon and have passed the runner who was running second. What position do you take now?

Second. If you answered that you are now first, then this is incorrect: you overtook the second runner and took his place, so you are now in second position

You are running a marathon and have passed the last runner. What position do you take now?

If you answered that it was the penultimate one, you were wrong again :). Think about how you can overtake the last runner? If you are running after him, then he is not the last. The correct answer is - it is impossible, you cannot overtake the last runner

There were three cucumbers and four apples on the table. The child took one apple from the table. How much fruit is left on the table?

3 fruits, and cucumbers are vegetables

The product first rose in price by 10%, and then fell in price by 10%. What is its value now relative to its original value?

99%: after the price increase, 10% was added to 100% - it turned out to be 110%; 10% of 110% = 11%; then subtract 11% from 110% and get 99%

How many times does the number 4 appear in the integers from 1 to 50?

15 times: 4, 14, 24, 34, 40, 41, 42, 43, 44 - twice, 45, 46. 47, 48, 49

You have driven your car two-thirds of the way. At the beginning of the journey, the car's gas tank was full, but now it is one quarter full. Will there be enough gasoline until the end of the trip (at the same consumption)?

No, because 1/4< 1/3

Mary's father has 5 daughters: Chacha, Cheche, Chichi, Chocho. What is the name of the fifth daughter?

A deaf and mute man went into a stationery store to buy a pencil sharpener. He stuck his finger into his left ear and made a spinning motion with the fist of his other hand near his right ear. The seller immediately understood what was being asked of him. Then a blind man entered the same store. How did he explain to the salesman that he wanted to buy scissors?

I just said, he's blind, but not dumb

A rooster has flown to the border between Russia and China. I sat down exactly on the border, absolutely in the middle. Layed an egg. It fell exactly across: the border divides it in the middle. Which country does the egg belong to?

Roosters don't lay eggs!

One morning, a soldier who had previously been on night guard approached the centurion and said that that night he had seen in a dream how the barbarians would attack the fortress from the north that evening. The centurion did not really believe in this dream, but still took measures. That same evening, the barbarians actually attacked the fortress, but thanks to the measures taken, their attack was repulsed. After the battle, the centurion thanked the soldier for the warning and then ordered him to be taken into custody. Why?

Because he slept on duty

There are ten fingers on the hands. How many fingers are there on ten hands?

A plane with English tourists was flying from Holland to Spain. He crashed in France. Where should the surviving (wounded) tourists be buried?

The survivors do not need to be buried! :)

You were driving a bus with 42 passengers from Boston to Washington. At each of the six stops, 3 people got out of it, and at every second - four. What was the driver's name when the driver arrived in Washington 10 hours later?

How about you, because at the beginning it was said that you were driving a bus

What can you find in minutes, seconds and days, but not in years, decades and centuries?

How many times can you subtract 3 from 25?

Once, because after the first subtraction the number "25" will change to "22"

Mrs. Taylor's entire bungalow is decorated in pink, with pink light fixtures, pink walls, pink carpets, and a pink ceiling. What color are the stairs in this bungalow?

There are no stairs in the bungalow

In the ancient castle where the prison was located, there were 4 round towers in which prisoners were imprisoned. One of the prisoners decided to escape. And then one fine day he hid in a corner, and when a guard came in, he stunned him with a blow to the head, and he ran away, changing into different clothes. Could this happen?

No, since the towers were round and there were no corners

The 12-story building has an elevator. Only 2 people live on the ground floor; from floor to floor the number of residents doubles. Which button in the elevator of this building is pressed most often?

Regardless of the distribution of residents by floor - button “1”

A pair of horses ran 20 kilometers. Question: How many kilometers did each horse run individually?

20 kilometers

What can stand and walk, hang and stand, walk and lie at the same time?

Is it possible to predict the score of a football match before it starts, and if so, how?

The score of any match before it starts is always 0:0

What can a person increase in diameter by 7 times in a few seconds?

Pupil. When transitioning from bright light to darkness, the diameter can change from 1.1 to 8 mm; everything else either hardly increases or increases in diameter by no more than 2-3 times

A seller at the market sells a hat that costs 10 rubles. A buyer comes up and wants to buy it, but he only has 25 rubles. The seller sends the boy away with these 25 rubles. change it to a neighbor. The boy comes running and gives 10 + 10 +5 rubles. The seller gives the hat and change 15 rubles, and 10 rubles. keeps it for himself. After some time, a neighbor comes and says that 25 rubles. fake, demands to give her money. The seller returns her money. How much money was the seller defrauded of?

The seller was deceived for a counterfeit 25 rubles.

How many animals did Moses take on his ark?

It was not Moses who took the animals into the ark, but Noah.

2 people entered the entrance at the same time. One has an apartment on the 3rd floor, the other on the 9th. How many times will the first person get there faster than the second? Note: They simultaneously pressed buttons on 2 elevators moving at the same speed.

The usual answer is 3 times. Correct answer: 4 times. Elevators usually go from the 1st floor. The first one will travel 3-1=2 floors, and the second 9-1=8 floors, i.e. 4 times more

This riddle is often offered to children. But sometimes adults can rack their brains for a long time to figure out how to solve such a problem, so you can organize a competition: invite everyone to try to solve the problem. Whoever guesses it, regardless of age, deserves a prize. Here's the task:

6589 = 4; 5893 = 3; 1236 = 1; 1234 = 0; 0000 = 4; 5794 = 1; 1111 = 0; 4444 = 0; 7268 = 3; 1679 = 2; 3697 = 2

2793 = 1; 4895 = 3

The main thing is to look at the problem like a child, then you will understand that the answer is 3 (three circles in the writing of numbers)

Two horsemen competed to see whose horse would reach the finish line last. However, things did not go well, both stood still. Then they turned to the sage for advice, and after that they both rode at full speed.

The sage advised the horsemen to exchange horses

One student tells another: “Yesterday our college basketball team won the basketball game with a score of 76:40. At the same time, not a single basketball player scored a single goal in this match.”

Women's teams played

A man walks into a store, buys sausage and asks to cut it, not across, but lengthwise. The saleswoman asks: “Are you a fireman?” - "Yes". How did she guess?

The man was in uniform

The lady did not have a driver's license with her. She did not stop at the railroad crossing, although the barrier was down, then, not paying attention to the “brick,” she moved along a one-way street against the traffic and stopped only after passing three blocks. All this happened in front of a traffic police officer, who for some reason did not consider it necessary to intervene.

The lady was walking

On one Odessa street there were three tailoring workshops. The first tailor advertised himself as follows: “The best workshop in Odessa!” The second is “The best workshop in the world!” The third “outdid” them both.

“The best workshop on this street!”

Two brothers were drinking at a bar. Suddenly, one of them began to argue with the bartender, and then pulled out a knife and, not paying attention to his brother’s attempts to stop him, hit the bartender. At his trial he was found guilty of murder. At the end of the trial, the judge said: “You have been found guilty of murder, but I have no choice but to let you go.” Why did the judge have to do this?

The culprit was one of the conjoined twins. The judge could not send a guilty person to prison without putting an innocent person there as well.

We were traveling in the same compartment: Baba Yaga, Zmey Gorynych, a stupid ensign and a smart ensign. There was a bottle of beer on the table. The train entered the tunnel and it became dark. When the train came out of the tunnel, the bottle was empty. Who drank the beer?

The stupid ensign drank the beer, since the other creatures are unreal and do not occur in life!)