Interesting tasks for children. Interesting and non-standard tasks for ingenuity

To solve the problems in this section, you do not need to have absolutely no mathematical knowledge, it is enough just to have some ingenuity and simple common sense.

Amazing Clock (Chinese Puzzle)

Once a house was urgently asked to go watchmaker.

I am ill, ”replied the watchmaker,“ and I cannot go. But if the repair is simple, I will send you my student.

It turned out that the broken arrows had to be replaced by others.

My student will cope with it, - the master told. - He will check the mechanism of your watch and pick up new hands to them.

The student was very diligent in his work, and when he finished inspecting his watch, it was already dark. Considering the work completed, he hastily put on the selected hands and put them on his watch: the big hand at number 12, and the small hand at number 6 (it was exactly 6:00 pm).

But soon after the apprentice returned to the workshop, to inform the master that the work was done, the telephone rang. The boy picked up the phone and heard the customer's angry voice:

You have badly fixed the clock, they incorrectly show the time.

The apprentice master, surprised by this message, hurried to the customer. When he arrived, the watch repaired by him showed the beginning of the ninth. The apprentice took out his pocket watch and handed it to the irate owner of the house:

Check, please. Your watch does not lag behind for a second.

The stunned customer had to agree that his watch at the moment really shows the correct time.

But the next morning the customer called again and said that the hands of the clock had obviously gone crazy and were walking around the dial as they pleased. Apprentice master ran to the customer. The clock showed the beginning of the eighth. Checking the time in his watch, he was seriously angry:

You are laughing at me! Your watch shows the exact time!

The clock really showed the exact time. The indignant apprentice master wanted to leave immediately, but the owner kept him. A few minutes later they found the cause of such incredible incidents.

Do not you guess what's the matter?

Clock stopped

One person did not have pocket watches, but there were only wall clocks that once stopped. He went to his acquaintance, whose clock was perfect, found out the time and, without stopping long, returned home. At home, he quickly made simple calculations and set the hands of the wall clock to the exact time.

How did he act and reason, if he did not previously know how long the road takes?

Two columns

Eight pieces of paper with the numbers 1, 2, 3, 4, 5, 7, 8 and 9 are arranged in two columns, as shown in the figure:

Having moved only two pieces of paper, you need to make sure that the sums of numbers in both columns become the same (the total number of pieces of paper in the columns should remain equal to 8).

Moscow - Tula

At noon, a bus with passengers goes from Moscow to Tula, traveling at a speed of 75 km / h. An hour later a cyclist leaves Tula for Moscow and drives along the same highway at a speed of 25 km / h. When the bus passengers and the cyclist meet, which of them will be farther from Moscow?

Envelope with money

Dad called his daughter, asked her to buy some of the things he needed to leave, and said that the money was in the envelope on the desk. The girl, glancing at the envelope, glimpsed the number 98 written on it, took out the money and, without counting it, put it in her bag, and crumpled the envelope and threw it away.

In the store she bought things for 90 rubles, and when she wanted to pay, it turned out that not only did she not have eight rubles left, as she supposed, but even four rubles were missing.

At home, she told the pope about it and asked if he had made a mistake when he counted the money. The father replied that he counted the money correctly, and she was mistaken herself. What was the girl's mistake?

Half term

In a certain kingdom, the king issued a decree:

“Let no one of the unfortunate prisoners in our prison spend more than one day more than half the time left to him!”

Explain the will of the king. It does not matter how much the prisoner was convicted, but if he was left to sit, for example, for 1 year, then he should be released in exactly six months. The decision, of course, is humane, but it put the prison director in a difficult position: what about the convicts for life, because the king’s will must be fulfilled exactly ...

What should the prison director do?

Note: It is of course not allowed to shorten the life of prisoners by violent means in such a situation.

At high tide

Not far from the coast stands a ship with a rope ladder launched into the water along the side. The staircase has 10 steps; the distance between the steps is 30 cm. The lowest step touches the surface of the water. The ocean today is very calm, but the tide begins, which raises the water by 15 cm per hour. How long does the third step of the rope ladder cover with water?

Card focus

The magician takes a pack of cards (52 pieces), turned upside down, counts 20 of them, turns them face down and passes them to the viewer. The spectator, having mixed upturned cards with the entire deck, carefully shuffles the deck so that the inverted cards are randomly distributed in it. Then, holding the deck under the table so that the cards are not visible, counts the top 20 cards and passes them to the magician.

The juggler, taking the pile and keeping it still under the table, says: “Now I’ll touch by touch to equalize the number of inverted cards in my part of the deck and in yours. To do this, I need to turn a few more cards. ” Then, after a small manipulation, he still draws his cards under the table, lays them on the table, counts upside down. There are exactly as many of them as among the 32 cards of the viewer.

What is the secret of this focus?

Incorrigible debater

I remember that there was one student in our group, an avid debater. For almost any reason, he offered to make bets, which, as a rule, won. So, he argued that he would be able to guess what the score would be in the match “Spartak” - “Torpedo” before the start of this match. Another time, he argued that in the beginning of a small international football tournament, no footballer will score a single goal. And imagine, won this dispute.

It must be admitted that sometimes he lost, but he was not very upset. I remember, he argued for a ruble with another student, that if he gives him 5 rubles, he will give 100 rubles. And lost it bet.

Since he considered himself a clairvoyant and denied it to everyone else, he offered the following bet as proof. He describes on paper some event that will occur, or not happen within the next 10 minutes. This note is placed on the table under an ashtray or other object. His rival, in turn, writes one word on paper: “yes” or “no.” It is clear that “yes” means that the intended event will occur, and “no” means that it will not. After 10 minutes, the notes are credited, and if the opponent of our student guesses, he gets 100 rubles, if he does not, then he pays the student 1 ruble. Could you guess which event was mentioned in the note of our student if he couldn’t lose in principle?

Schoolchildren on the bus

Schoolchildren of the 3rd class of a Moscow school made a bus excursion to Volokolamsk. One of them, telling the house about this trip, drew the following picture:

Is it possible to determine from this picture where the bus is going to Moscow or Volokolamsk?

Election of the Secretary General

At the founding congress of the party "Nomenclature for Democracy" to be held the election of the general secretary of the party. In accordance with the regulations, the elections are held according to a two-step scheme: if at the first stage no candidate obtains more than half of the votes, then the second round is held, in which two candidates compete with the highest number of votes in the first round.

All delegates to the congress were divided into three factions: "New Wave", "Servants of the People" and "Fundamentalists", which include respectively 40%, 32% and 28% of all delegates to the congress. Each of the factions nominated their own candidate, respectively Akseleratov, Baranov and Volkov. It is also known that in the event of failure of their candidate in the second round, supporters of A mostly support B, supporters of B in this case will split roughly in half between A and B, and finally supporters of C will support B.

Some tasks that are easily solved by children can be very difficult and even unbearable for adults. Similar tasks, the solution of which will require the use of logic, are waiting for you further.

  1. Four-digit numbers

Preschool children solve this problem in 5-10 minutes. Programmers - for 1 hour. Most people with higher education ... However, check for yourself. And try to be honest, do not rush to find a ready answer (it will be at the end, under all other tasks).

Little hint: try to think outside the box.




Do not figure it out? There are 2 more tips for you (read the first one first - if it doesn’t help, go to the second one).
  1) Remember who is the fastest to solve this problem? Preschoolers. And why? Think like them.
  2) Think "visually." This is not a math problem.

2. Parking

Another elementary question - this time from the Hong Kong test for admission to primary school. The "thoughtless" graduates of the kindergarten are given a decision of 20 seconds!

3. Numerical pyramid

Hello again from Singapore. Try to catch up in your mind with local third-graders who easily cope with the mathematical problem below. (But if you get stuck, do not worry much: as shown by the television survey, adults found it “difficult”, “too abstruse” and even “insoluble”!)

4. Chocolate box

And now fast forward to the United States. Here is one of the test assignments for ordinary Washington 7th graders (12-13 years old by local system).
  “There is 50 chocolates in a box. Of these, 30 with caramel, 25 with coconut, 10 - with caramel, and with coconut, and the rest without filling.

Question: Which chart correctly reflects the contents of the box? "

5. Family ties

  And finally, a mystery that is not even related to mathematics. Nevertheless, it puzzles many adults, while children almost instantly give the correct answer!
  “Father and son have an accident. The father perishes on the spot. The son in critical condition is taken to the hospital for surgery. The surgeon looks at the child in horror and says: “I cannot operate it! This is my son!"

Question: How is this possible?

Answers and solutions

1. Four-digit numbers
The answer is: 2581 = 2
  In each group of 4 numbers, it was only necessary to count the closed circles. For example, the number 6 has one circle, the number 8 has two. So the number 6889 has six of them. And so on.

2. Parking
Answer: 87
  It was enough just to mentally turn the picture upside down.

3. Numerical pyramid
  Answer: D = 1345; E = 2440
First of all add two numbers in the bottom row: 198 + 263 = 461
  It turned out the amount is greater than the number that stands above them: 461\u003e 446
  Subtract less from the larger: 461 - 446 = 15
  In the same way, we count the other pairs and see that everywhere it turns out 15. Ta-dam! That is the key to the solution.

4. Chocolate box
  Answer: diagram B
Simple arithmetic:
  How many chocolates with caramel? 30 - 10 = 20
  How many chocolates with coconut? 25 - 10 = 15
  How much chocolate is left without the filling? 50 - (20 + 15 +10) = 5

5. Family ties
Answer: the surgeon is the mother of the child.

Task 1.

A father with a sly smile asks his first-grade son a question: give me the largest number.
  Having received the answer, he just shakes his head in surprise, not knowing what to say.
  What did the son answer?

Task 2.

What is the sign to put between the numbers 4 and 5,
  so that the result is more than four,
  but less than five?

Task 3.

There is a road on which only one car can drive.
  Two cars are driving along the road: one from the mountain, the other downhill.
  How do they disperse?

Task 4.

How many times can you subtract three from the damn dozen?

Task 5.

Two approached the river at the same time.
  The boat on which you can cross, can withstand only one person.
  And yet without help, everyone crossed over on this boat to the other side.
  How did they do it?

Task 6.

In the company of friends, it occurred to one to offer them a dispute:
- Guys, I now put the bottle in the middle of the room and crawl into it.
And he did it ... he won.
How did he do it?

Task 7.

On the table in a row are 6 glasses.
  The first three are empty, and the last three are filled with water.
  How to make empty glasses and full alternate with each other, if you can touch only one glass (you can not push a glass with a glass)?

Task 8.

You participate in competitions and overtake a runner who occupies the second position.
  What is your position now?

Task 9.

Three swallows flew out of the nest.
  What is the probability that in 15 seconds they will be in the same plane?

Task 10.

They put the pencil on the floor and asked several people to jump over it.
But no one could do it. Why?

Answers to tasks on wit:

1.Thirty first (meaning the date of the month).

2. The comma.

3. And why should they leave?
  They are both down (downhill and downhill).

4. From the damn dozen, the number three can be deducted only once,
  first, since any further subtraction will be made from a smaller number.

5. They came to different banks of the river.

6. He crawled into her - into the room.

7. Take the fifth glass, pour the contents into the second glass and put the glass in place.

8. The second.

9.100%, because three points always lie on the same plane.

10. He was laid next to the wall (close).

JOKES, STEELS, PUZZLES, TASKS ON CONSTRAINTS.

The kids really like joking tasks, puzzles, logical tasks. We give them at the end of classes to enhance the attention of children.

  Three boys - Kolya, Andrey, Vova - went to the store. On the way, they found three pennies. How much money would one Vova have found if he went to the store?(3 kopecks)

The length of the log is five meters. One minute from this log saw off on one meter. How many minutes will the log be cut?(in 4 minutes).

A flock of geese flew: one goose in front, and two behind; one behind and two in front; one between two and three in a row. How many were the geese? (3 geese)

In a basket 4 apples. Divide them between the four children so that each child receives an apple and one apple would remain in the basket.(3 will take an apple and 1 basket of apples)

Two fathers and two sons ate 3 eggs at breakfast, and each of them got a whole egg. How could this happen?(grandfather, father, son were sitting at the table)

How many ends have 4 sticks? 5 sticks? And 5 and a half sticks?(8,10,12)

A field plowed 7 tractors. 2 tractors stopped. How many tractors are in the field?(7 tractors)

There were 7 brothers, each brother had one sister. How much was the man going?(8 people)

December came. 3 daisies were bloomed, and then another 1. How many flowers are bloomed?(December flowers do not bloom)

Chocolate is divided into several parts. Andrew ate 2 parts, Alenka 3 parts, 1 part remained. How many pieces of chocolate was divided?(in 6 parts)

  The animal has 2 right legs, 2 left, 2 legs in front, 2 behind. How many legs does an animal have?(4 legs)

  The shoemaker decided to fix 2 pairs of shoes. On each heel, he will fill the taps, each taps he will nail with two nails. How many nails and nails will he need?(4 heels, 8 nails)

  How many nuts are in an empty glass?  (no one)

7 ducks swam in the pond. They decided to play and dived into the depths. How many ducks swam in the pond? (7 ducks)

In the vase there are three daisies and 8 cornflowers. How many daisies in a vase? (3 daisies)

9 girls poured on one bed in the garden. How many beds did the girls water? (9 beds)

2 brothers drew on 2 drawings as a gift to the grandfather. How many drawings did grandpa get?   (4 pictures)

Three goats were walking. 1 - in front of two, 1 - between two, 1 - behind two. How did the kids go? (one after another)

Mistress once came from the bazaar,

The hostess from the bazaar brought home:

Potatoes, cabbage, carrots,

Peas, parsley and beets ...

She laid out all the vegetables separately. How many plates are required for them?(6 plates)

Alenka and Tanya have 4 pencils each. Alena gave Tanya 2 pencils. How many pencils did each girl have? (Tanya - 6, Alena - 2)

In the barrel - 10 spoons of honey. How many children can taste this honey? (1 spoon - 10 children, half a spoon - 20 children, 2 spoon - 5 children)

Sister and brother received 4 candies each. Sister ate 3 pcs., And brother 2 pcs. who has more candy? (at my brother's)

Sister is 4 years old, brother is 6 years old. How old will your brother be when your sister turns 6? (8 years)

  Goose weighs 2 kg. How much will he weigh if he stands on one leg?(2 kg)

  One donkey carried 10 kg of sugar, and another donkey carried 10 kg of cotton wool. Who had the luggage heavier?(it is the same)

  From under the gate you can see 8 cat's paws. How many cats are in the yard?

(2 cats)

8 squirrel tails peeped out of the hollow. How many squirrels in the hollow? (8 squirrels)

At 12 o'clock at night it began to snow. Can there be a few days at the same time sunny weather? (no, because the sun does not shine at night)

The blacksmith shod three horses. How many horseshoes did he have to make? (12 horseshoes)

There were seven old men,

They have seven pososhkov,

On each hitch seven knots,

There are seven knots on each bitch,

In each knot seven pies.

Each pie has seven sparrows

Each sparrow has seven tails.

How old were there?(7 oldies)

Can it rain 2 days in a row? (no, t.to  between two days night

Which figure has no beginning or end? (in a circle, in an oval)

One person was asked how many children did he have? The answer was: "I have 6 sons, and everyone has a sister." How many children does he have? (7 children)

You and I, yes we are with you. How many of us all? (Two)

On the table were 4 apples, one of them was cut in half. How many apples are on the table? (4 apples)

In the plate were three carrots and four apples. How many fruits were on the plate? (4 apples, carrots are vegetables)

In the chandelier 5 lights were burning. Two of them went out. How many bulbs are left in the chandelier? (five)

  Mother has a daughter, Dasha, son Sasha, dog Druzhok and Cat Fluffy. How many children does mom have?(two children)

There are three apples on one plate, as many on the second, and as many on the third as on the second. How many apples are there on the third plate? How many apples are there in total? (3 and 9)

  Lena has four textbooks in her briefcase, Sasha has the same number, Masha has the same number as Sasha. How many textbooks are in Masha's portfolio? How many textbooks do all three students have?(4 and 12)

  Grandmother knitted 5 hats to grandchildren, as many scarves, and blouses as many as hats and scarves together. How many blouses grandmother knitted? How many things are connected?(10 and 20)

  Dima and Vasya must solve four problems. Dima solved two problems, and Vasya - three. Who are the boys left to solve more problems?(Dima)

  A strip of paper needs to be cut into four pieces. How many cuts do you need?(three cuts)

  How many newspapers will dad read per week if he reads one newspaper every day?(7 newspapers)

  Four eggs are boiled for four minutes. How many eggs are boiled?

(4 minutes)

To five boys were able to ride, not enough two bikes. How many bicycles cost around the house?

(3 bicycles)

So that seven girls could begin to embroider, three needles are missing. How many needles are there in a needle case?   (4 needles)

At the table sawed off one corner. How many corners does he have now? And how many corners will be if sawn off two, three, four corners? (5 corners, 6, 7, 8.)