Law on the Protection of Consumer Rights No. 2300-1 of February 7, 1992 (Articles 18 and 25) gives the right to a consumer who discovers any defects in the purchased product to return the product to the seller or exchange the product for another, and in the case when The purchased product is not suitable based on external features (color, style, etc.), it can be exchanged for another similar product. This rule applies to any payment method for purchased goods. That is, when goods are purchased with borrowed bank funds under a consumer lending agreement, the rule will work.

But, in connection with the emergence of new obligations under the concluded loan agreement, some additional points appear. An additional complicating point may be the concluded collateral agreement to secure the loan; in this case, all actions to dispose of the purchased goods, including its return, are agreed upon with the bank, in accordance with the Civil Code of the Russian Federation (clause 1 of Article 334.1, clause 2 of Article 346 ). Let's figure it out how to return or exchange goods purchased on credit according to the Consumer Protection Law.

Terms of the loan agreement and agreement on pledge of goods

The consumer lending agreement may contain a provision on the procedure for returning and exchanging goods. If there is such a provision in the agreement, in it, according to paragraphs 4, 9 and 10 of Art. 5, art. 11 of Law No. 353-FZ of December 21, 2013, there may be conditions for terminating the loan agreement on the basis of termination of the purchase and sale agreement, as well as a period for notifying the bank about the early repayment of the loan amount.

The Civil Code of the Russian Federation (Article 346, paragraph 2) describes the legal procedure for the alienation of purchased goods and the return of the deposit.

You must demand to terminate the contract for the purchase and sale of goods, return the goods or exchange them for a similar product or for a product of the same brand.

When expressing a demand to return the goods upon termination of the contract, you must indicate in the claim the details of your bank account for the transfer of funds for the return to pay for the loan for the goods. If a defective product is returned, interest under the consumer loan agreement and other payments under the agreement will be transferred to this account. According to the Consumer Protection Law No. 2300-1 (Article 22, paragraph 6 of Article 24), the amount must be returned within ten days from the date of receipt of your claim.

The claim is made in writing in two copies, one of which, with the seal and signature of the person who accepted the claim from you, you keep for yourself. You can submit your claim in person or send it by registered mail with acknowledgment of receipt and a list of the contents.

If the seller refuses to accept the claim, it can be submitted in the presence of two witnesses. Witness testimony that the seller refused to accept the claim will have weight in the future.

If a low-quality product is returned, the seller must, at his own expense, conduct an examination of its quality (see Law No. 2300-1, paragraph 5 of Article 18).

The act of returning the goods together with the seller’s representative and receiving money for the goods

A document confirming to the bank that the goods have been returned to the seller is an act of return of goods.

If the goods are not returned but exchanged, the seller must issue you new documents for the goods.

If a return is made, the seller must return to the buyer part of the price of the product, which the buyer made as a down payment. The money is returned to the buyer’s bank account (if the initial payment was paid by card), or transferred to him from the store’s cash register.

If the buyer returns a low-quality product, then the seller will transfer interest and payments under the loan agreement to the buyer after receiving payment documents that confirm the fact that the consumer has paid bank interest and payments under the loan agreement.

When a consumer returns a product purchased on credit, only the sales contract is terminated. The loan agreement has not yet been terminated, so payments under it continue until termination, otherwise penalties will be imposed by the bank, according to Art. 811 of the Civil Code of the Russian Federation.

We contact the bank to terminate the loan agreement and collateral agreement

You must write an application to the bank, listing the following facts:

1. An application for early termination of a loan agreement and a pledge agreement on the basis of termination of a contract for the purchase and sale of goods is written if the goods purchased on credit are returned to the seller without exchange or replacement.
2. An application to change the loan agreement and collateral agreement is written in the case when you exchanged or exchanged goods from the seller.

When returning a purchase to the bank, you must proceed according to the following procedure:

1. Submit to the bank an act of return of goods, a claim for return of goods to confirm the fact of return.
2. Return to the bank the loan amount and accrued interest for the past period of using the loan.
3. Obtain from the bank a certificate about the full cost of the loan, as well as about the execution of the loan agreement and about the closure of the loan account.
4. If the amount in the loan account is more than needed for early repayment of the loan, you must submit an application for the release of funds. The difference is issued by the bank without opening additional accounts and without paying a commission.

If a consumer exchanges a low-quality product or replaces it with a similar one, he must submit the following documents to the bank:

1. Certificate of return of goods and claim for return of goods.
2. Documents for the new product provided to you by the seller.

Please note that if you repay the loan early, you must notify the bank 30 calendar days in advance, unless otherwise specified in the consumer loan agreement itself (see Parts 3, 4, Article 11 of Law No. 353-FZ). However, if less than 30 days have passed since the loan was opened, this rule does not apply and you can close the loan early without notice.

It is not your fault that the product was not purchased and its expiration date has expired.
It is your responsibility not to sell expired goods! This is why you may be subject to disciplinary action - your employer. And Rospotrebnadzor, if detected, will impose an administrative fine.

But nowhere does it stipulate your obligation to pay your employer the cost of expired goods. Neither in the job description, nor in the agreement on swearing. responsibility, nor in laws.
If you are forced to pay, this suggests that you are thereby forced to sell expired goods that threaten the life and health of the population!

You need to file a complaint with Rospotrebnadzor, the state. labor inspectorate. And submit an application to the employer - manager. The manager may give you a written answer or not answer at all; just a signature in the copy of the application or an outgoing number confirming your appeal.

Labor Code - Labor Code of the Russian Federation - Chapter 39. MATERIAL RESPONSIBILITY OF AN EMPLOYEE

Article 238. Material liability of the employee for damage caused to the employer. The employee is obliged to compensate the employer for direct actual damage caused to him. Unreceived income (lost profits) are not subject to recovery from the employee. Direct actual damage is understood as a real decrease in the employer’s cash property or deterioration in the condition of said property (including property of third parties owned by the employer, if the employer is responsible for the safety of this property), and also the need for the employer to make costs or excess payments for the acquisition, restoration of property or compensation for damage caused by the employee to third parties. Part three is no longer in force. - Federal Law of June 30, 2006 N 90-FZ.

Article 239. Circumstances excluding the financial liability of the employee. The employee's financial liability is excluded in cases of damage arising due to force majeure, normal economic risk, extreme necessity or necessary defense, or the employer's failure to fulfill the obligation to provide adequate conditions for storing property entrusted to the employee.

Article 240. The employer’s right to refuse to collect damages from the employee. The employer has the right, taking into account the specific circumstances in which the damage was caused, to fully or partially refuse to recover it from the guilty employee. The owner of the organization's property may limit the specified right of the employer in cases provided for by federal laws, other regulatory legal acts of the Russian Federation, laws and other regulatory legal acts of the constituent entities of the Russian Federation, regulatory legal acts of local government bodies, and the constituent documents of the organization.

Article 241. Limits of employee’s financial liability. For damage caused, the employee bears financial liability within the limits of his average monthly earnings, unless otherwise provided by this Code or other federal laws.

Article 242. Full financial liability of the employee. The full financial liability of an employee consists of his obligation to compensate for direct actual damage caused to the employer in full. Material liability in the full amount of damage caused may be assigned to the employee only in cases provided for by this Code or other federal laws. Employees under the age of eighteen bear full financial liability liability only for intentional damage, for damage caused while under the influence of alcohol, drugs or other toxic substances, as well as for damage caused as a result of a crime or administrative violation.

Article 243. Cases of full financial liability. Financial liability in the full amount of damage caused is assigned to the employee in the following cases:
1) when, in accordance with this Code or other federal laws, the employee is held financially liable in full for damage caused to the employer during the performance of the employee’s job duties;
2) shortage of valuables entrusted to him on the basis of a special written agreement or received by him under a one-time document;
3) intentional infliction of damage;
4) causing damage while under the influence of alcohol, drugs or other toxic substances;
5) damage caused as a result of the employee’s criminal actions established by a court verdict;
6) damage caused as a result of an administrative violation, if established by the relevant government body;
7) disclosure of information constituting a secret protected by law (state, official, commercial or other), in cases provided for by federal laws;
8) damage caused while the employee was not performing his job duties. Financial liability in the full amount of damage caused to the employer can be established by an employment contract concluded with the deputy heads of the organization, the chief accountant.

Article 244. Written agreements on full financial responsibility of employees Written agreements on full individual or collective (team) financial responsibility, that is, on compensation to the employer for damage caused in full for the shortage of property entrusted to employees, can be concluded with employees who have reached the age of eighteen years and directly servicing or using monetary, commodity valuables or other property. Lists of works and categories of workers with whom these contracts can be concluded, as well as standard forms of these contracts are approved in the manner established by the Government of the Russian Federation.

Article 245. Collective (team) financial liability for damage. When employees jointly perform certain types of work related to the storage, processing, sale (release), transportation, use or other use of valuables transferred to them, when it is impossible to differentiate the responsibility of each employee for causing damage and to conclude an agreement with him on compensation for damage in full, collective (team) financial liability may be introduced. A written agreement on collective (team) financial liability for damage is concluded between the employer and all members of the team (team). Under an agreement on collective (team) financial liability, values ​​are entrusted to a predetermined group of persons, to whom full financial responsibility for their shortage is assigned. To be released from financial liability, a member of a team (team) must prove the absence of his guilt. In case of voluntary compensation for damage, the degree of guilt of each member of the team (team) is determined by agreement between all members of the team (team) and the employer. When recovering damages in court, the degree of guilt of each member of the team (team) is determined by the court.

Article 246. Determination of the amount of damage caused. The amount of damage caused to the employer in the event of loss and damage to property is determined by actual losses, calculated on the basis of market prices prevailing in the area on the day the damage was caused, but not lower than the value of the property according to accounting data, taking into account the degree of wear and tear of this property. Federal law may a special procedure will be established for determining the amount of damage subject to compensation caused to the employer by theft, intentional damage, shortage or loss of certain types of property and other valuables, as well as in cases where the actual amount of damage caused exceeds its nominal amount.

Article 247. The employer’s obligation to establish the amount of damage caused to him and the cause of its occurrence. Before making a decision on compensation for damage by specific employees, the employer is obliged to conduct an inspection to establish the amount of damage caused and the reasons for its occurrence. To conduct such an inspection, the employer has the right to create a commission with the participation of relevant specialists. Requesting a written explanation from the employee to establish the cause of the damage is mandatory. In case of refusal or evasion of the employee from providing the specified explanation, an appropriate act is drawn up. (Part two as amended by Federal Law No. 90-FZ of June 30, 2006) The employee and (or) his representative have the right to familiarize himself with all inspection materials and appeal them in the following manner: established by this Code.

Article 248. Procedure for collecting damages. Recovery from the guilty employee of the amount of damage caused, not exceeding the average monthly earnings, is carried out by order of the employer. The order can be made no later than one month from the date of final determination by the employer of the amount of damage caused by the employee. If the month period has expired or the employee does not agree to voluntarily compensate for the damage caused to the employer, and the amount of damage caused to be recovered from the employee exceeds his average monthly earnings, then recovery can only be carried out by the court. If the employer fails to comply with the established procedure for collecting damages, the employee has the right to appeal the employer’s actions in court. An employee who is guilty of causing damage to the employer can voluntarily compensate it in full or in part. By agreement of the parties to the employment contract, compensation for damage by installments is allowed. In this case, the employee submits to the employer a written obligation to compensate for damages, indicating specific payment terms. In the event of the dismissal of an employee who has given a written commitment to voluntarily compensate for damage, but refused to compensate for the specified damage, the outstanding debt is collected in court. With the consent of the employer, the employee can transfer to him equivalent property to compensate for the damage caused or correct the damaged property. Compensation for damage is carried out regardless of bringing the employee to disciplinary, administrative or criminal liability for actions or inactions that caused damage to the employer.

Article 249. Reimbursement of costs associated with employee training. In the event of dismissal without good reason before the expiration of the period stipulated by the employment contract or agreement on training at the expense of the employer, the employee is obliged to reimburse the costs incurred by the employer for his training, calculated in proportion to the time actually not worked after completion of training, unless otherwise provided by the employment contract or training agreement.

Article 250. Reduction by the labor dispute resolution body of the amount of damage to be recovered from the employee. The labor dispute resolution body may, taking into account the degree and form of guilt, the financial situation of the employee and other circumstances, reduce the amount of damage to be recovered from the employee. Reduction of the amount of damage to be recovered from the employee is not paid if the damage was caused by a crime committed for personal gain. PART FOUR

6th grade

6.1.

6.2.

cutting example).

6.3.

6.4.

boxes

6.5.

Why did she decide this?

7th grade

7.1. Find some natural number such that if you add the sum to it

its digits, it will be 2222.

7.2. Mom bought 10 large cakes, 7 medium ones and 4 small ones. Small

a cake weighs half as much as a medium one, and a large one weighs three times as much as a small one. How

mother divide them between six children so that the total weight of the cakes received

everyone, was the same, if she doesn’t want to cut the cakes?

7.3. The train, moving at a constant speed, had covered 1.2 times the distance by 17:00,

than by 16:00. When did the train leave?

7.4. How to cut a 6x6 checkered square into four equal ones

perimeter figures 16 each, if you can only cut on the sides of the cells?

The side of the cell is 1.

7.5. Twenty-seven classmates ate candy during the first and second breaks,

Moreover, at the second break, everyone ate one more candy than at the first. Peter

said that he counted the total number of candies eaten and received the answer 210.

Did he count correctly? Explain your answer.

6th grade

6.1. Find all three-digit numbers whose second digit is four times larger than the first.

and the sum of all three digits is 14.

6.2. A central 1x1 square was cut out of a 5x5 checkered square. Cut

the remaining figure into 4 equal checkered pieces. (Give one

cutting example).

6.3. From the apple box they took half of the total number of apples, then another half

the remainder, then half of the new remainder, and finally half of the next remainder.

After this, there are 10 apples left in the box. How many apples were in the box at the beginning?

6.4. Three boxes contain Christmas balls: one contains two red ones, the other contains a red one.

and blue, in the third there are two blue balls. The boxes say: "Two red", "Red

and blue", "Two blue". It is known that none of the inscriptions are correct.

How can you determine which box contains which balls by pulling out just one ball?

Indicate which box it should be taken from and how to determine the contents later

boxes

6.5. Three friends brought candy to school. The second brought twice as much

sweets than the first, and the third - three times more than the first. They added it all up

candy together. After the friends ate 3 candies, the first one left, and the second

I divided the remaining candies equally. The third told the second that she was mistaken.

Why did she decide this?

8th grade

8.1.

What is the wholesale price of the pen?

8.2.

8.3. a and b , satisfying the equality

a 2 +b=b 2 + a

8.4.

8.5.

9th grade

9.1. Find the area of ​​a square whose vertices all lie on two straight lines:

x+ y= 0 and x+ y= 2 .

9.2. On a small island, 2/3 of all men are married and 3/5 of all women are married.

How many people on the island are married if there are 1,900 people living there?

9.3. On a circle with diameter AB and point C is chosen as the center O so that

angle bisector CAB perpendicular to the radius O.C. . In what respect is the straight line CO

divides angle ACB?

9.4. Find the number of three-digit numbers whose decimal notation involves

exactly one digit 3.

9.5. Mom wants to punish Petya for failing in math. They agreed on

next. Petya thinks of a two-digit number with different digits and reports it

mom. After this, mom tells Petya her two-digit number. Petya adds

mom’s number to your number, then to the amount received, then to the amount received again

amount, etc. until he gets a sum ending in two

the same numbers. Will mom be able to stop Petya from playing football that day?

8th grade

8.1. The merchant bought a batch of pens at the wholesale market and offers customers either

one pen for 10 rubles, or three pens for 20 rubles. Moreover, in both cases he

receives the same profit (the difference between buying a product and selling it).

What is the wholesale price of the pen?

8.2. In a right triangle, the bisector of an acute angle is equal to one of two

the segments into which she divided the opposite side. Prove that she

twice as long as the second of these segments.

8.3. Find the sum of two different numbers a and b , satisfying the equality

a 2 +b=b 2 + a

8.4. Three students A, B and C were competing in the 100m race. When A reached the finish line, B

was 10m behind him, also when B finished, C was 10m behind him.

How many meters was A ahead of C at the finish line?

8.5. At Masha’s birthday party, each of the 10 guests had an equal amount of

sweets During the tea party, the first ate one candy, the second - two, the third - three, and

etc., tenth – 10 candies. Masha wanted to shift the

candies so that again everyone has an equal amount of candy in front of them, but dad,

without looking at the table, he said that she couldn’t do it. Why did he decide this?

Preview:

6th grade

6.1. Answer. 149 and 284.

If the first digit is not less than 3, then the second is not less than 12, which is impossible. Means,

6.2. One example is shown in Figure 1. This example is not the only one.

Rice. 1

6.3. Answer. 160 apples.

When half of the apples are taken from the box, half of the apples remain in it.

the amount that was before. This means that before this there were twice as many apples.

Therefore, at the beginning there were 10x2x2x2x2 = 160 apples in the box.

6.4. Answer. From the Red and Blue box.

It follows from the condition that this box contains either two blue balls or two red ones. Taking out

one ball, we will know the contents of this box. If there are two blue balls in it, then

the one on which it says “Two red” will have multi-colored balls, since it does not contain

two red (according to condition) and not two blue (they are in the first box). In box with

The inscription “Two blue” means two red balls. If we took out a red ball, then

similarly, in the “Two Blue” box there are multi-colored balls, and in the “Two Red” box

- blue balls.

6.5. Answer. Because the number of remaining candies must be odd.

The total number of candies brought is even. This can be explained this way: second

the girl brought an even number of sweets - this follows from the condition. And the first and

the third is the number of candies of the same parity (because triple an odd number is odd, and triple an even number is even). This means the total is an even number of candies. Otherwise - algebraically. The number of sweets brought is x 2 x 3 x 6 x 2 3 x - even number. The girls ate 9 candies during recess - an odd number. Therefore, they must have an odd number of candies left, and they will not be able to divide it equally.

7th grade

7.1. Answer. 2209.

2209 + (2 +2 + 0 + 9) = 2222.

7.2. Answer. For example, like this: give five people two large cakes and one

the middle one, and the sixth - two medium ones and all four small ones.

Let m – the weight of a small cake, then the average one weighs 2 m, and large - 3 m.

The total weight of all cakes is: 4 m 7 2 m 10 3 m 48 m , so one child

you should get cakes with a total weight of 8 m.

7.3. Answer. At 11:00.

If the distance covered by the train by 16:00 is S , then by 17:00 he had passed the distance 1, 2 S.

This means that in the last hour the train has passed 0.2S , that is, a path of length S he passes in 5

hours. The initial movement time is 16 – 5 = 11 (hours).

7.4. The answer is shown in Figure 2.

Rice. 2

7.5. Answer.

7.5. Answer. He made a mistake.

The sum of two consecutive numbers is the sum of two numbers of different parities, and

therefore it is odd. This means that each of the classmates ate an odd number of candies.

Classmates are an odd number (27), and the sum of an odd number of odd

numbers is odd and cannot equal 210.

8th grade

8.1. Answer. 5 rub.

If x – the wholesale price of a pen, then when selling one for 10 rubles. the seller receives

profit 10 – x (rub.). Selling three pens for 20 rubles. he makes a profit of 20 – 3 x

(rub.). According to condition 10 – x = 20 – 3 x, from where x = 5 (rub.).

8.2. Let AL – bisector of an acute angle CAB right triangle ABC

(ACB 90) and, by convention, AL BL. Then if CAB 2, then LAB, and therefore ABL . Sum of acute angles of a triangle ABC is equal to 3, hence 30.

Then in a right triangle ACL the leg opposite the angle of 30 is equal to

half of the hypotenuse, from where

CL AL . The statement has been proven.

8.3. Answer. 1.

Let's transform this equality: a 2 b 2 (a b ) 0 or (a b )(a b 1) 0 . By

condition, these numbers are different. Therefore the first parenthesis is not zero. Means,

a b 1 0, whence a b 1.

8.4. Answer. At 19 m.

It follows from the condition that the student’s speed B A , a

student speed C is 0.9 of the student's speed B . It follows that

student speed C is 0.81 of the student's speed A. So, when A runs

100m, student C will run 81m.

8.5. Answer. Because the number of remaining sweets was odd, that is, it could not

divide by 10.

At the beginning, the number of candies was even, since it was divisible by 10. The total number of candies eaten at the beginning is 1 + 2+ 3 + ... + 10 = 55 - an odd number.

Therefore, the number of remaining candies is odd, as the difference between even and odd

numbers.

9th grade

9.1. Answer. 2.

The side length of this square is the distance between the lines x y 0 and x y 2, so

as on each of the straight lines there are two vertices of the square. And this distance is equal

distance from the origin to the straight line x y 2 , intersecting the coordinate axes at a distance of 2 from the origin. This means that the required distance is the height in

an isosceles right triangle with legs of length 2, which is equal to 2.

9.2. Answer. 1200 people.

Let x – number of men, y – the number of women on this island. From the condition

follows that

x y, in addition, x y 1900 . Solving this system, we get:

x 900, y 1000 . Hence the number of married men is equal to

900 600

And the general

the number of married people is 1200.

9.3. Answer. 2:1.

Angle bisector CAO is the height of the triangle CAO, therefore CA AO. But

O.A.O.C. – as radii, which means a triangle CAO – equilateral. Then

ACO 60. Moreover, in an isosceles triangle OCB (OC OB)

COB 120, so OCB 30 (otherwise you can get it by using

because ACB – based on the diameter, equal to 90).

9.4. Answer. 225.

If a three-digit number has 3 in the first place, then the other two digits are

arbitrary, different from 3. This means that any of the other 9 can be in second place

digits, and on the third - any of the 9 other digits - a total of 9x9 = 81 options. If three

is in second place, then any number except 3 and 0 can be in first place, and on

the last - any, except three. In total we get 8x9 = 72 options. As many

we will get options if the three is in last place. Total: 81 + 72 +

72 = 225 options.

9.5. Answer. Will be able.

If Petya thinks of a number with two digits of different parities, then his mother needs to name,

for example, the number 20. Then the parity of each of the last two digits after each

the increase will continue, and these numbers will never coincide. If the numbers

Petya's numbers will be of the same parity, then mom just needs to name the number 50. After

every two additions, the last two digits will be repeated, i.e. will not

coincide, and after the first (third, fifth, etc.) addition these numbers will be

have different parities, i.e. won't match either.

Task 1:

Solve the puzzle: AX × YX = 2001.

(A. Blinkov)

Solution:

Answer: AX = 29, YX = 69 or, conversely, AX = 69, YX = 29. Since 2001 = 3 23 29, the number 2001 can be represented as a product of two-digit numbers only in the following ways: 69 29 or 23 87 .

Task 2:

Ofenya (peddler, peddler) bought a batch of pens at the wholesale market and offers customers either one pen for 5 rubles, or three pens for 10 rubles. Ofenya receives the same profit from each buyer. What is the wholesale price of the pen?

(A. Sablin)

Solution:=2

Answer: the wholesale price of a pen is 2 rubles 50 kopecks. If the wholesale price of a pen is x rubles, then 5 - x = 10 - 3x, whence x = 2.5.

Task 3:

Natasha and Inna each bought the same box of tea bags. It is known that one bag is enough for two or three cups of tea. Natasha's box was enough for only 41 cups of tea, and Inna - only 58 cups. How many bags were in the box?

(A. Spivak, I. Yashchenko)

Solution:=3

Answer: 20 sachets.

First decision. Since Inna drank 17 cups of tea more than Natasha, it means that she made three cups of tea from at least 17 bags. The remaining 7 = 58 - 17 3 cups could be obtained only in one way: 2 bags for 2 cups each and 1 bag for 3 cups. This means there were 17 + 3 = 20 bags in the box. At the same time, Natasha prepared 2 cups of tea from 19 bags, and 3 cups of tea from the twentieth.

Second solution. Note that there could not be more than 20 bags: if there were at least 21 bags in the pack, Natasha could not drink less than 2 21 = 42 cups of tea. But there couldn’t be less than 20 bags, otherwise Inna would have drunk no more than 3 19 = 57 cups. This means that each pack could only contain 20 sachets. Inna used 18 sachets 3 times, and Natasha only 1.

Task 4:

Arrange 6 different numbers in a circle so that each of them is equal to the product of the two adjacent ones.

(A. Mityagin)

Solution:=4

If the numbers a and b are next to each other, then the next number is b/a, followed by 1/a, then 1/b, and finally a/b. These six numbers satisfy the condition of the problem. Of course, if the choice of numbers a and b is unsuccessful, some of the indicated numbers will coincide, but this will not stop us: to solve the problem, it is enough to present one example. For example, take a = 2, b = 3.

Task 5:

Vifsla, Tofsla and Hemul played snowballs. Tofsla threw the first snowball. Then, in response to each snowball that hit him, Vifsla threw 6 snowballs, Hemulen - 5, and Tofsla - 4 snowballs. After some time the game ended. Find out who was hit by how many snowballs if 13 snowballs flew past the target. (They don’t throw snowballs at themselves.)

(T. Golenishcheva-Kutuzova, V. Kleptsyn)

Solution:=5

Answer: Khemul, Vifsla and Tofsla were hit once each. If Vifsla, Tofsla and Hemulya were hit by x, y and z snowballs respectively, then a total of 13 + x + y + z snowballs were thrown (since 13 snowballs did not reach the target). On the other hand, Vifsla threw 6x, Hemulen threw 5y, and Tofsla threw 4z + 1 snowballs (along with the first snowball). We get the equation

6x + 5y + 4z + 1 = 13 + x + y + z, whence 5x + 4y + 3z = 12. Since x, y, z are non-negative integers, x can be 0, 1 or 2, y - 0 , 1, 2 or 3, z - 0, 1, 2, 3 or 4. By searching we find solutions (1,1,1), (0,3,0) and (0,0,4). But, since you cannot throw snowballs at yourself, there cannot be two zeros among the numbers x, y, z. Therefore, only the first case is possible.

Task 6:

The fields of a checkered board measuring 8 × 8 will be painted red one by one so that after each subsequent cell is painted, the figure consisting of painted cells has an axis of symmetry. Show how you can paint over a) 26; b) 28 cells, observing this condition. (As an answer, place numbers from 1 to 26 or to 28 on those cells that must be painted in the order in which the coloring was carried out.)

(I. Akulich)

Solution:=6

The answer is shown in the figure.

Content

Task 1. (7 points)

The sum of its digits was added to the number and we got 2017. Give an example of such a number.

Examples: 2012, 1994. Other numbers are not suitable.

Criteria. Any of these numbers given: 7 points.

Any other number given: 0 points.

Task 2. (7 points)

The girl replaced each letter in her name with its number in the Russian alphabet. The resulting number is 2011533. What is her name?

Answer: Tanya.

There may be other sequences of letters, but only one of them is a name.

Criteria. Received the name Tanya: 7 points.

Any other sequence of letters received: 0 points.

Task 3. (7 points)

The seller purchased a batch of pens and sold them. At the same time, some buyers bought one pen for 10 rubles, and some bought 3 pens for 20 rubles. It turned out that the seller received the same profit from each purchase. Find the price at which the seller purchased the pens.

Answer: 5 rubles.

Solution. Let the purchase price of the pen x. Then the profit per pen is 10 — x, for 3 pens 20 — 3x. Solving Equation 10 — x= 20 — 3x, we get x= 5.

Criteria.

It is not justified that the purchase price of the pen should be 5 rubles, but it is verified that in this case the condition is met: 4 points.

Only the correct answer without any explanation: 2 points.

Task 4 (7 points)

The student spider pulled the web between 11 points so that his webs did not intersect anywhere, and in the end he returned to the starting point. The spider-teacher praised him and only noticed that real masters observe the same conditions, but they draw the “correct” web, in which no segments lie on the same straight line. Help the spider connect all 11 dots in the picture with the “correct” web.

Solution. One possible method is given below.

Criteria. Any correct example: 7 points.

An example in which some segments lie on the same line, but none neighboring segments do not lie on the same straight line: 4 points.

An example in which there are adjacent segments lying on the same straight line: 0 points.

Task 5. (7 points)

A square window opening is formed by two rectangular frames. Inside each of them they wrote a number equal to the perimeter of the frame. Write what the square side of the entire window opening is and explain how you got it.

Answer: 5.

Solution. Let the side of the square be a, and the width of the left rectangle is b. Then the width of the right rectangle is a— b.

The left rectangle gives the ratio 2 a+ 2b= 14, and the right rectangle gives the ratio 2 a+2a— 2b= 16. Adding these two ratios together, we get 6 a= 30, from where a= 5.

Criteria. Correct solution by any means: 7 points.

The solution is logically correct, but due to an arithmetic error the answer is incorrect: 3 points.

An example was selected where the rectangles actually have the required perimeter, but it was not explained how the lengths of their sides were obtained: 2 points.

Only correct answer without explanation: 1 point.