Tasks for logical thinking. Interesting logic question. Difficult logic questions

Let's brainstorm! 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 a lack of experience or preparation. Even a truly experienced developer can easily "stumble" over the solution of some cleverly tailored puzzle. Therefore, we will not talk about how to write a resume and present yourself profitably. We focus on solving non-trivial problems, which include the solution of a logical and / or mathematical nature.

"Toughie"

Remember the riddle from the third movie? If not, then remember, as Microsoft likes to regale this question.

A task:

There are 2 empty buckets: the first is 5 liters, the second is 3 liters. How to measure 4 liters of water with their help?

First, fill a five-liter bucket. Next, pour water from it into a three-liter so that 2 liters of water remain in the five-liter (completely filling the three-liter). Pour out all the water from the smaller bucket and pour the remaining 2 liters into it. Refill the 5 liter bucket and pour one liter into the 3 liter bucket (it will just fill up): this leaves 4 liters of water in the larger bucket.

Jars with pills

A task:

There are twenty jars of pills. Almost all tablets weigh 1 g, and only one weighs 1.1 g. We have accurate scales with which you 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 away and imagine that we have 2 jars, one of which contains heavier pills. Even if we put them both 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 🙂 this case the weight will be 2.1 or 2.2 (depending on how many pills we took). So we define our jar.

Let's return to the task. From each jar you need to get different amount tablets. That is, from the first jar 1 tablet, from the second - 2, from the third - 3 and so on. If each tablet weighed 1 g, total weight would be 210 g. But since the tablets are heavier in one of the jars, the weight will be more. To determine the desired jar, simply use the formula:

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

But the interesting logic does not end there. Move on!

Date

A task:

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

Nothing complicated: pure mathematics. If a girl's clock is fast, and she thinks that they are behind, then she will hurry up and come for 5 minutes. before. The guy, on the contrary, will consider that he has another 5 minutes of time left, which is why these same 5 minutes. will be late.

We count the weight of the chicken

A task:

The length of the 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, measured along the lateral 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

A task:

The book contains N pages, which are numbered standardly: 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 digit in place of one, so there are N digits in place of one. But after 9, two-digit numbers begin, and we need to add N-9 digits. Same with three digits that start after 99: add N-99 digits. It makes no sense to continue, since the amount does not imply more than 999 pages. We get the following formula:

Mathematical tasks at interviews are also quite simple, but often only at first glance. Try mentally dividing 30 by 1/2 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 it:

Number 3

A task:

How many integers in the range 1-1000 can contain the number 3? Do not use a computer while counting.

And then there is a group of numbers (there are 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 has a triple in place of tens: 33, 133 ... 933. We remove another 9, leaving 81 numbers. Here is some simple math:

100 + 90 + 81 = 271

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

1000 - 729 = 271

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

There is a rich house and a poor one. They are on fire. Which house will the police put out?

Police do not 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 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 in the off state. 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 a while one of them will turn off. Enter the room. One bulb will be hot from the switch on, the second - warm from the off, the third - cold, from the untouched switch

It is known that among the nine coins there is one counterfeit, which has less weight than the rest of the coins. How to determine a counterfeit coin using a weighing pan in two weighings?

1st weighing: 3 and 3 coins. The counterfeit coin is in the pile that weighs the least. 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 fake is the remaining coin.

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

They were on different shores

Two fathers, two sons found three oranges and divided them. Each 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 and not break?

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

The man was driving a large truck. The lights on the car were not on. There was also no moon. 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 for one cat to catch one mouse?

Five minutes

Can you light a match underwater?

You can, if you pour water into some kind of container, for example, into a glass, and keep the match below the glass

The boat is rocking on the water. A ladder has been thrown out from it along the side. Before high tide, water covered only the bottom step. After how much time will water cover the 3rd step from the bottom, if at high tide the water arrives at 20 cm per hour, and the distance between the steps is 30 cm?

Never, as the boat rises with the water

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

Give one girl an apple with a basket

One and a half pike perch cost one and a half rubles. How much are 13 zanders worth?

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

The potter was alone, because:

If there were no potters, then the merchants would have to tell the truth that all other merchants, and this contradicts the condition of the problem.
If there were more than one potter, then each potter would have to lie that the rest were merchants.

There are two coins on the table, in total they give 3 rubles. One of them is not 1 ruble. What are these coins?

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 either in the letter “a” or in the letter “ya”: Anna, Maria, Irina, Natalya, Olga, etc. However, there is only one woman's name, which ends with another 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 that in 72 hours it will be sunny?

No, because in 72 hours it will be night

Seven brothers have a sister. How many sisters are there?

One yacht goes from Nice to San Remo, the other from San Remo to Nice. They left the harbors at the same time. The first hour of the yacht's movement went at the same speed (60 km/h), but then the first yacht increased its speed to 80 km/h. Which of the yachts will be closer to Nice at the time of their meeting?

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

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

Only the woman went to Moscow, the rest went the other way

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

None - 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 is the smoke coming from the chimney?

You are running a marathon and you overtook the second runner. What is your current position?

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

You are running a marathon and you overtook the last runner. What is your current position?

If you answered that the penultimate one, you were mistaken again :). Think about how you can overtake the last runner? If you run after him, then he is not the last. The correct answer is it's impossible, you can't overtake the last runner

There were three cucumbers and four apples on the table. The child took one apple from the table. How many fruits are 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 the original?

99%: after a rise in price, 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 integers from 1 to 50?

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

You drove the car two thirds of the way. At the beginning of the journey, the gas tank of the car was full, and now it is one-quarter full. Will there be enough gasoline until the end of the journey (at a similar consumption)?

No, since 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 dumb man went into an office supply store to buy a pencil sharpener. He stuck his finger in his left ear and with the fist of his other hand made rotary motion near your right ear. The seller immediately understood what he was being asked for. Then a blind man entered the same store. How did he explain to the salesperson that he wanted to buy scissors?

Just said he's blind but not dumb

A rooster flew to the border of Russia and China. He sat right on the border, absolutely in the middle. Took an egg. It fell exactly across: the border divides it in the middle. What 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 dreamed that the barbarians would attack the fortress that evening from the north. The centurion did not really believe in this dream, but nevertheless he took measures. That same evening, the barbarians really attacked the fortress, but thanks to 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?

For sleeping on duty

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

Aircraft with English tourists flew from Holland to Spain. It crashed in France. Where should the surviving (injured) tourists be buried?

The survivors do not need to be buried! :)

You drove 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 name of the driver when the driver arrived in Washington 10 hours later?

How about you, because in the beginning it was said that you drove the bus

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

How many times can 3 be subtracted from 25?

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

All of Mrs. Taylor's bungalows are finished in pink color: it has pink lamps, 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 day he hid in a corner, and when the guard came in, he stunned him with a blow to the head, and he ran away, changing into other clothes. Could this be?

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

The 12-storey 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 house is pressed more often than others?

Regardless of the distribution of residents by floors - 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 down 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 in a person can increase in diameter by 7 times in a few seconds?

Pupil. When moving from bright light to dark, the diameter can change from 1.1 to 8 mm; everything else either almost does not increase, or increases in diameter by no more than 2-3 times

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

The seller was deceived by fake 25 rubles.

How many animals did Moses take on his ark?

Animals were taken to the ark not by Moses, but by Noah

2 people walked in 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 person arrive faster than the second? Note: they simultaneously pressed the buttons in 2 elevators moving at the same speed.

Usual answer: 3 times. Correct answer: 4 times. Elevators usually go from the 1st floor. The first one will pass 3-1=2 floors, and the second one 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 guess how to solve such a problem, so you can arrange a competition: invite everyone to try to solve the problem. Whoever guesses, regardless of age, deserves a prize. Here is 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 in a childish way, then you will understand that the answer is 3 (three circles in the numbers)

Two jigits competed: whose horse will come to the finish line last. However, things did not go well, both stood still. Then they turned to the sage for advice, and after that both galloped at full speed.

The sage advised the jigits to exchange horses

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

Women's teams played

A man enters a store, buys sausage and asks to cut it, but not across, but along. The saleswoman asks: "Are you a firefighter?" - "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 even though the barrier was lowered, then, ignoring the "brick", she moved along the one-way street against the traffic and stopped only after passing three blocks. All this happened in front of the traffic police officer, who for some reason did not consider it necessary to intervene.

The lady was walking

There were three tailor shops on one Odessa street. The first tailor advertised himself like this: “The best workshop in Odessa!” The second - "The best workshop in the world!" The third "surpassed" them both.

“The best workshop on this street!”

The two brothers were drinking at a bar. Suddenly, one of them began to argue with the bartender, and then he pulled out a knife and, ignoring 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 are 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 Siamese twins. A judge couldn't send a guilty person to jail without putting an innocent one in there too.

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

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

Riddles with a trick - riddles with a simple question and a non-standard answer. At first glance, the answer may seem strange and wrong, but if you carefully read the riddle and think about the answer, it will turn out to be quite logical. Trick riddles are usually not without a sense of humor. They not only develop ingenuity and out of the box thinking but also provide fun. Tell riddles with a trick to your friends and relatives, have a fun and useful time.

The same person always came to the football match. Before the start of the game, he guessed the score. How did he do it?
Answer: Before the start of the game, the score is always 0:0
78835

More than an hour, less than a minute.
Answer: Second (hand of some watch models)
Tag. Anna
47090

What language is spoken silently?
Answer: sign language
134251

Why is the stopcock red on trains and blue on planes?
Answer: Many will say, "I don't know." Experienced will answer: "There is no stop valve on airplanes." In fact, the plane has a stopcock in the cockpit.
Makarova Valentina, Moscow
31534

The boy paid 11 rubles for a bottle with a cork. A bottle costs 10 rubles more than a cork. How much does a cork cost?
Answer: 50 cents
Orlov Maxim, Moscow
40063

One French writer terribly disliked the Eiffel Tower, but he constantly dined there (on the first level of the tower). How did he explain it?
Answer: This is the only place in all the vast Paris, from where it is not visible.
Borovitsky Vyacheslav, Kaliningrad
37536

What city are you hiding in? male name and side of the world?
Answer: Vladivostok
Mezhuleva Julia
43297

Seven sisters are in the country, where each is busy with some business. The first sister is reading a book, the second is cooking, the third is playing chess, the fourth is doing Sudoku, the fifth is doing the laundry, the sixth is taking care of the plants. And what does the seventh sister do?
Answer: plays chess
Gobozov Alexey, Sochi
43316

Why do they go often, but rarely go?
Answer: stairs
172814

It goes uphill, then downhill, but remains in place.
Answer: Road
134606

Which word has 5 "e" and no other vowels?
Answer: immigrant
Radaev Evgeny, Petrozavodsk
39695

Two people approach the river. Near the shore is a boat that can only support one. Both men crossed to the opposite bank. How?
Answer: They were on different shores
25 25, Vladivostok
29916

Vasily, Peter, Semyon and their wives Natalya, Irina, Anna have been together for 151 years. Every husband is 5 years older than his wife. Vasily is 1 year older than Irina. Natalya and Vasily together are 48 years old, Semyon and Natalya are together 52 years old. Who is married to whom, and how old is who? (Age must be expressed in whole numbers).
Answer: Vasily (26) - Anna (21); Peter (27) - Natalia (22); Semyon (30) - Irina (25).
Chelyadinskaya Victoria, Minsk
18342

Jackdaws flew, sat on sticks. They sit down one by one - the jackdaw is superfluous, they sit two by two - the stick is superfluous. How many sticks were there and how many jackdaws were there?
Answer: Three sticks and four jackdaws
Baranovsky Sergey, Polotsk
24974

Where is it found that a horse jumps over a horse?
Answer: Chess
)))))))) Renesmee, L.A
34920

Which table has no legs?
Answer: Diet
Boyko Sasha, Wolf
29498

Do not write anything or use a calculator. Take 1000. Add 40. Add another thousand. Add 30. Another 1000. Plus 20. Plus 1000. And plus 10. What happened?
Answer: 5000? Wrong. The correct answer is 4100. Try to recalculate on a calculator.
Ivanova Daria, Daria
32759

How can a person not sleep for 8 days?
Answer: sleep at night
Sone4ka0071, Sosnogorsk
33267

What animal do people walk on and cars pass by?
Answer: zebra
Kostryukova Tanya, Saransk
25913

Which word "no" is used 100 times?
Answer: Groan
Muslimova Sabina, Dagestan (Derbent)
30877

What is an elephant without a nose?
Answer: Chess
Prokopyeva Xenia, Moscow
26795

Mr. Mark was found murdered in his office. The cause was a bullet wound to the head. Detective Robin, inspecting the scene of the murder, found a cassette recorder on the table. And when he turned it on, he heard the voice of Mr. Mark. He said, “This is Mark. Jones just called me and said that in ten minutes he would be here to shoot me. It's useless to run. I know this tape will help the police arrest Jones. I hear his footsteps on the stairs. Here the door opens... The assistant detective offered to arrest Jones on suspicion of murder. But the detective did not follow his assistant's advice. As it turned out, he was right. Jones wasn't the killer, as was said on the tape. Question: why did the detective have suspicions?
Answer: The cassette in the voice recorder was being revised at the start. Moreover, Jones would have taken the cassette.
Katarina, Moscow
10754

Sherlock Holmes was walking down the street. And suddenly he saw a dead woman lying on the ground. He walked over, opened her bag and took out her phone. In tel. book, he found her husband's number. He called. He speaks:
- Urgently come here. Your wife is dead. And after a while the husband arrives. He looks at his wife and says:
- Oh, honey, what happened to you?
And then the police arrive. Sherlock points his finger at the woman's husband and says:
- Arrest this man. It was he who killed her. Q: Why did Sherlock think that?
Answer: Because Sherlock didn't tell her husband the address.
Tusupova Aruzhan
18835

Two fifth-graders Petya and Alyonka are walking from school and talking.
“When the day after tomorrow becomes yesterday,” one of them said, “today will be as far from Sunday as the day that was today, when the day before yesterday was tomorrow.” What day of the week did they speak?
Answer: Sunday
Piggy, Ololoshkino
13915

There is a rich house and a poor one. They are on fire. Which house will the police put out?
Answer: Police don't put out fires, firefighters put out fires
78023

On what path has no one ever walked or traveled?
Answer: Milky Way
Tikhonova Inessa, Aktobe
22962

How many years in a year?
Answer: one (summer)
Maxim, Penza
28103

What kind of cork can not plug a single bottle?
Answer: road
Volchenkova Nastya, Moscow
23417

In what word is the drink and the natural phenomenon “hidden”?
Answer: grapes
anufrienko dasha, khabarovsk
22895

What sign must be placed between 6 and 7 so that the result is less than 7 and greater than 6?
Answer: comma
Mironova Violetta, Saratov
20271

Without which nothing ever happens?
Answer: Untitled
Anyutka, Omsk
23689

Union, number then preposition -
That's the whole charade.
And so that you can find the answer,
We need to remember the rivers.
Answer: i-hundred-k
nazgulichka, ufa
16389

What is the strongest muscle in the human body?
Answer: The common opinion is the language. In fact, the calf and chewing muscles.
Anonymous
17960

You can tie, but you can't untie.
Answer: conversation
Dasha, Chelyabinsk
21922

To what mere mortal even the president takes off his hat?
Answer: hairdresser
Nastya Slesarchuk, Moscow
20662

How to put 2 liters of milk in a liter jar?
Answer: Turn it into curd
Anonymous
18034

Once upon a time there was one orphan girl in the thicket, she had only two kittens, two puppies, three parrots, a turtle and a hamster with a hamster that was supposed to give birth to 7 hamsters. The girl went for food. She goes through the forest, field, forest, field, field, forest, forest, field. She came to the store, but there was no food there. Goes on, forest, forest, field, field, forest, field, forest, field, forest, field, field, forest. And the girl fell into the hole. If she gets out, dad will die. If she stays there, her mother will die. The tunnel cannot be dug. What should she do?
Answer: She is an orphan
I'm Yulechka, Omsk
14097

They are metallic and liquid. What are we talking about?
Answer: nails
babicheva alena, moscow
14902

How to write "duck" in 2 cells?
Answer: In the 1st - the letter "y", in the 2nd - a dot.
Sigunova 10 years old Valeria, Zheleznogorsk
20501

Name a word in which one letter is a prefix, the second is a root, the third is a suffix, the fourth is an ending.
Answer: Gone: y (prefix), sh (root), l (suffix), a (ending).
Malec Daniel
14462

Guess the riddle: who has a heel behind his nose?
Answer: Shoes
lina, Donetsk
17425

There were 20 people on the bus. At the first stop, 2 people got off and 3 people got in, at the next one, 1 got off and 4 got in, at the next, 5 got off and 2 got in, at the next, 2 got off and 1 got in, at the next, 9 got off and no one got in, at the next - 2 more came out. Q: How many stops were there?
Answer: The answer to the riddle is not that important. This is a riddle with an unexpected question. While you are telling the riddle, the guesser begins to mentally count the number of people on the bus, and at the end of the riddle, you will confuse him with a question about the number of stops.
39610

Husband and wife lived. The husband had his own room in the house, which he forbade his wife to enter. The key to the room was in the bedroom dresser. So they lived for 10 years. And so the husband went on a business trip, and the wife decided to go into this room. She took the key, opened the room, turned on the light. The wife walked around the room, then saw a book on the table. She opened it and heard someone open the door. She closed the book, turned off the light and closed the room, putting the key in the chest of drawers. This is the husband. He took the key, opened the room, did something in it and asked his wife: “Why did you go there?”
How did the husband guess?
Answer: The husband touched the light bulb, it was hot.
SLEPTSOVA VIKUSIA, OMSK
11930

There were husband and wife, brother and sister, and husband and brother-in-law. How many people?
Answer: 3 people
Arkharov Mikhail, Orekhovo-Zuevo
14795

The full name is Danuta. How does it sound abbreviated?
Answer: Dana
Khanukova Danuta, Bryansk
12866

A river that "fits" in your mouth?
Answer: Gum
Bezusova Anastasia, Overyata village

Preschoolers solve this problem in 5-10 minutes. For some programmers, it takes up to an hour to complete it. But many people, after writing a few sheets of paper, give up.

Parking space number

A six-year-old child usually takes no more than 20 seconds to solve this problem. But unprepared adults, she often enters into a stupor. So what number is hidden under the car?

A riddle for a genius

A genius finds a solution in 10 seconds. Bill Gates - in 20 seconds. Graduate of Harvard (Harvard University) - in 40 seconds. If you found the answer in 2 minutes, then you belong to the top 15% of the most gifted people. 75% of people are not able 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 keep the appearance of justice, he issued an order according to which anyone who wants to settle on the island should, after thinking well, make any statement, and after a preliminary warning that his life depends on the content of this statement. The order read: “If the stranger tells the truth, he will be shot. If he tells a lie, he will be hanged." Can an alien become a resident of the island?

Project approval

According to the agreement, the procedure for approving a new project, in the development of which institutions A, B, C participate, is as follows: if A and B participate in the approval first, then institution C must also join the participation. 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 C would take part in it, while the participation of institution B would not be necessary (while maintaining an agreement on the procedure for approving projects)?

Two tribes

Two tribes live on the island: well done. Who always tell the truth, and liars who always lie. The traveler met an 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 what tribe he belonged to. The guide returned and said that he claims to be from a tribe of fellows. The question is: was the conductor a good fellow or a liar?

Aborigines and aliens

Before the court are three people, of which each can be either an aborigine or an alien. The judge knows that natives always answer questions truthfully, and aliens always lie. However, the judge does not know which of them is an aborigine 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 about what the first answered. The second says that the first said that 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 the 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 over to the other side through the end of the tape)?

Purchase

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

Tourist

The tourist walked to the lake. He came to 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. Two guys were sitting at the crossroads, one of them always told the truth, the second always lied. Both of them answered any question with either "yes" or "no". All this was known to the tourist, 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 put only one question to one of the guys. What was the question, since he knew from the answer which road leads to the lake?

broken window

There were nine students left in the class during the break. One of them broke the window. The teacher's question was answered as follows:

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 have 30 seconds to think.

Project approval procedure

The enterprise has three workshops - A, B, C, 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 participates in approval of the project, then shops A and C take part in it. The question is: under these conditions, is shop C obliged to take part in the approval of the project, when shop A participates in the approval?

An evening walk

Which of these nine mustaches went on an "evening walk"?

7 buttons

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

Make a table

In the Moscow semi-finals of the European Basketball Championship, held in Soviet time, places are distributed in the following way: 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 position. Each team received 2 points for a win, 1 point for a loss, and 0 points for a no-show. Draws were not allowed. Make a summary table of the results of the games if it is known that the Finnish team won against the Italian team and lost to the Romanian team.

Explanation is inevitable

On Tuesday, at about 10 am, a stranger burst into Inspector Warnicke's room. He was extremely excited. His hands were trembling, his tousled hair stuck out in all directions. A few minutes later, after lighting a cigarette and calming down, the visitor began his story: - This morning I returned from vacation. All night I had to shake on the train. I didn't get enough sleep and when I got home I decided to lie down on the sofa. From fatigue, I did not immediately notice that the piano had disappeared from the room, and the coffee table and armchair had been moved. On this sheet of paper, I drew a plan for the arrangement of the furniture in the room before I left. - Here's what, dear, - said Inspector Varnicke, glancing briefly at the drawing, - First of all, it's quite 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 Varnicke doubt the veracity of the visitor's story?

LOGIC TASKS

Logic tasks, as well as mathematics, is called "mind gymnastics". But unlike mathematics, logic puzzles is an entertaining gymnastics, which in a fun way allows you to test and train thought processes, sometimes in unexpected angle. To solve them, you need quick wits, sometimes intuition, but not special knowledge. Solving logic problems 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 in which you just need to get used to, feel the situation, visualize it and catch the connections.

Even the most challenging tasks on logic 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 decision on the surface is not always the right one. But more often than not, solving a logic problem turns out to be much simpler than it seems at first glance, despite the confusing condition.

Interesting logic tasks 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 tasks for weighing, transfusion, tasks for non-standard logical thinking help in Everyday life solve everyday problems in a non-standard way.

In the process of decision logic tasks you will get to know 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 the work "Analytics" Aristotle created 20 schemes of reasoning, which he called syllogisms. One of his most famous syllogisms is: “Socrates is a man; all men are mortal; So Socrates is mortal. Logic (from other Greek. Λογική - speech, reasoning, thought) is the science of correct thinking, or, in other words, "the art of reasoning."

There are certain methods solving logic problems:

way of reasoning, which solves the simplest logical tasks. 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.

tables way, used in solving text logic problems. As the name implies, solving logical problems consists in building tables that allow you to visualize the condition of the problem, control the process of reasoning, and help draw the right logical conclusions.

graphs way consists in enumeration options development of events and the final choice of the only right decision.

flowchart 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 the block diagram, which is essentially a program, the execution of which leads to the solution of the task.

billiard way follows from the theory of trajectories (one of the sections of probability theory). To solve the problem, it is necessary to draw a billiard table and interpret the actions of the movements of the billiard ball along different trajectories. It is necessary to keep records possible outcomes 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 with a variety of logical tasks for grades 1, 2, 3, 4, 5, 6, 7, 8, 9. We have selected for you the most interesting logic puzzles with answers which will be interesting not only for children, but also for parents.

choose for the child logic puzzles according to his age and development
do not rush to open the answer, let the child find it himself logical solution tasks. Let him come to the right decision himself and you will see what pleasure and a sense 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.

With our selection logical tasks with answers you will really learn how to solve logical problems, expand your horizons and significantly develop logical thinking. Dare!!!

Logic problem solving — the first step in 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 saying

Logic is the morality of thought and speech.

Jan Lukasiewicz

How do you feel about taking a break from the gray routine for a few minutes and stretching your brain a little? Then choose any interesting logic question from this article and try to find the answer to it yourself. Just be careful not to peep into the answers right away - this is not only dishonest, but also uninteresting!

Mental workout for toddlers

Many of these mysteries have been well known since Soviet times, but still do not lose their relevance. The answers to them are so simple and obvious that it is almost impossible to guess right away. Ready? Then full speed ahead!

1. “Why do you go to bed when you want to sleep?” The whole "chip" of this question lies precisely in the wording. After all, if you say it out loud, the brain immediately perceives the first two words as one. Why? Well, how is this "why"? You can lie down on the bed, cover yourself with a blanket, close your eyes and ... And, by the way, the correct answer is "On the floor."

2. "When can a person be in a room without a head?" Another logic question with an elementary answer. However, it can be very difficult for a child to reach the right decision, because not even every adult can immediately guess what happens when we stick our head out the window.

3. "Can an ostrich call itself a bird?" You may be surprised, but no special knowledge from the field of zoology is needed in order to correctly answer this question, because even the most educated and erudite ostrich will not be able to name himself in any way. At least because he can't speak.

4. “Which words have a hundred consonants?” And here the child will undoubtedly become thoughtful. After all, it is difficult to even imagine such a word - as many as 100 consonants, and if you add vowels as well? What kind of lexical monster is this? But the correct answer, as always, lies on the surface - “STOL”, “STOP”, “STOP”, “STOP”, “STOP”.

5. “In front of you is a bathtub filled with water. On the edge lies a mug and a spoon. What should be used to quickly remove all the water from the bath? Think it's a mug? Because she's bigger? But a rational person, looking at your torment, will silently come up and pull out the cork.

6. “Three little pigs were walking through the forest. One walked ahead of the two, one behind them all, and one between the two. How did they go? To be honest, even adults often cannot answer such questions of logic with a catch. In fact, the pigs in this riddle are just following each other.

7. “The bull plowed the field all day. How many footprints did he eventually leave on the arable land? In fact, the bull leaves no traces at all, because the plow that he pulls behind him erases them.

8. “At 12 o'clock in the morning there is a torrential downpour. Could it be that after 72 hours there will be warm, sunny weather? No theory of probability will help you here, relax. But knowing how many hours in a day will help - there can be no sunny weather. If only because after the indicated 72 hours it will be midnight again.

So, we have considered some curious logic questions for children. And now let's move on to other, more complex and interesting tasks.

Other logic puzzles

We bring to your attention other interesting questions on logic that can make you think not only for kids, but also for their parents.

Wordplay

“On the seashore lay a stone, on the surface of which a word of 8 letters was scratched. When the rich read this word, they began to cry, the poor, on the contrary, rejoiced, and couples in love parted. What was that word? We will not comment on the answer in any way, because everything will become clear by itself. And the word was - "Temporarily."
“What word has 3 letters “l” and 3 letters “p” at once? - "Parallelepiped".

For math connoisseurs

“How much earth is in a hole 3 meters in diameter and 5 meters deep?” Still trying to count and looking for density different types soil? Don't forget that this is a question of logic. Already by the fact of its existence, the pit is empty, otherwise it would not be a pit.
"How many times can you subtract 6 from 30?" Don't share, take away! Only one, because next time you will subtract 6 not from 30, but from 24.

Vital

“Two friends were walking around the city and suddenly stopped, starting to argue. One began to assert that "this is red." Another objected to him and said that "this is black." The first was not at a loss and asked: "Why, then, is she white?", To which he heard: "Yes, because she is green." What were they talking about?" Correct answer to this riddle- currant.
“Three centuries ago, this procedure was carried out at a distance of 50 meters. Now this distance has been reduced by 10 times, and all thanks to the invention of a Soviet scientist, which you have probably seen more than once. What is it?" Nothing comes to mind? In fact, we are talking about a table for checking eyesight, also known as

American scientists, who came across this picture and questions to it, considered that this is one of the most effective IQ tests in the history of mankind. Take a close look at the image, and then try to give the correct answer to just 9 questions.

Questions

How many tourists stayed at this camp?
How long ago did they come here: today or a few days ago?
How far is the camp from the nearest settlement?
How did the tourists get here?
What time of day is it now?
Where does the wind blow: from the south or from the north?
Where did Shura go?
Give the name of the person who was on duty yesterday.
What is the date and what month?

Right answers

Breaking your head? Well, time to reveal the cards and demonstrate how elementary the answers are to even the most difficult logic questions:

Four. To understand this, just look at the list of attendants (it has four lines), as well as the number of plates and spoons on the mat.
Not today, because between the tree and the tent, a nimble spider managed to weave a cobweb.
It is unlikely, because the guys were able to bring with them live chicken(or she ran into them by accident, which, however, does not change the essence).
On the boat. Near the tree you can see a couple of oars, and since there were not very many cars in Soviet times, this is the most logical answer.
Morning, because the shadow falls to the west, and therefore the sun shines from the east.
This question on logic really requires additional knowledge. For example, you need to remember that on the south side of the tree the branches are always longer than on the north. Next you need to look at the fire - it deviates slightly towards the north, which means that the wind blows from the south.
Shura went to catch butterflies - from behind the bushes you can see a net falling on a winged beauty.
As you can see, Shura went for butterflies, and the boy sitting near the backpack with the letter "K" is Kolya. That is, two options already disappear. Another boy is taking pictures surrounding nature. He also cannot be on duty. But what is his name? Looking closely, you can see that in the backpack with the letter "B" is a tripod - an indispensable attribute of the photographer. We conclude that the name of the photographer begins with the same letter, which means that Vasya is photographing. By the method of elimination, we find out that Petya is on duty today, and from here we come to the conclusion that Kolya was on duty yesterday.
The answer to this question is closely related to the previous one. So, Petya is on duty today. Near his name, the number 8 is written on the board - the 8th number. As for the month, the very situation in the picture suggests that it takes place in August - only then do watermelons appear in our latitudes. Of course, there are also in September. But it can be quite difficult to find butterflies in early autumn, and the first fallen leaves appear on the ground.

Interesting? Did you know that only 6% of people can answer all 9 questions correctly? If you succeeded, you can accept congratulations, because this means that your IQ is 130 or more.