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. Petya

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 it contains two blue balls, 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 – an 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 was wrong.

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 from this 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 candies 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

it 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 9 others can take 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. The same amount

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

72 = 225 options.

9.5. Answer. He can.

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. they won't

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

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

Sell ​​me this pen - this is the question that new candidates are asked when they go for an interview. This is a standard technique that is very effective. Within a minute, the second recruiting agent (or who is conducting the interviews?) will be able to understand whether the candidate is suitable. People's reactions to this question are as follows:

1. The first category of people are lost and don’t understand what to do. They were caught off guard and have no idea what to say or how to sell the damn pen (sorry for the jargon).
2. The second category of candidates use template expressions like: this is a very good pen that will never let you down. The ink is of high quality, and the pen itself is high quality and reliable! Buy it, and you definitely won’t regret it.
3. The third category is creative and artistic individuals, who in the end will definitely get a job. Their answers to questions like “sell me a pen” are non-standard and original. They make even the most experienced recruiters who have heard a variety of versions admire them.

Simple example?

Understand the point: to sell a pen to a person, first of all you need to motivate him to buy, i.e. should make you want to buy it. Here's a simple example:

- sell me this pen (the recruitment agent will tell you and at the same time will definitely offer his pen - you will have to sell it);

(here you need to motivate him to buy)

- Fine. Would you give me your autograph? (you tell me)

- Yes, but I don’t have a pen (the interlocutor will answer. He gave it to you).

– then buy mine (you will answer and offer the item of trade).

Your interlocutor will have no choice but to buy a pen, because he promised to give you an autograph.

Here is a simple example - a video from the wonderful film “The Wolf of Wall Street” (I recommend watching it):

This is the method that is very effective at the moment, but in reality, sooner or later it will become hackneyed.

Another example of selling a pen at an interview

The big boss was hiring a young man. As expected, he asked to sell him a pen. This was a very cool pen (most likely a valuable gift), expensive and with a gold outline.

The candidate naturally agreed. He tried to praise it and offer it in different ways to his boss, but he refused, explaining his position by saying that he already had a pen.

“Okay, if you don’t want to buy, you don’t need to,” answered the young man;

“You gave up quickly,” the chief answered;

“Then it’s time for me to leave (gets up and leaves),” the candidate answers;

“Wait!” the boss shouts, “you have to give me my pen;

– yeah, I see that you’ve changed your mind. You're lucky, I'm already willing to sell the pen at half price;

– stop joking, I need my pen! Give her back now. Otherwise I'll call security;

- take it. But keep in mind: I was able to motivate you,” the young man answered, gave the pen and left.

The boss thought for a while and realized that this was the best candidate of all with whom he was able to interview. Later it was he who got the job.

Instead of conclusions

In order to sell a pen at an interview, you need to motivate your interlocutor to buy. The easiest way to do this is to ask for an autograph or do as the young man did. There is no point in praising her tritely - this is not what recruitment agents expect. Preference is given to people who were able to show creativity and ingenuity.

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; it is enough to include 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 charged with financial liability 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) causing damage 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 of June 30, 2006 N 90-FZ) The employee and (or) his representative have the right to familiarize himself with all inspection materials and appeal them in accordance with the procedure 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