61 shLgZh Skis 71 SzGzh CiGara

62 shLDt LaDya 72 SzT SiTo

63 shLKkh Leika 73 sZKkh LANGUAGE

64 shLChsch Luch 74 SzChsch SaChok

65 shLPb Lupa 75 sZpB Tooth

66 ShlshL ShiLo 76 SzshL Sol

67 shLSz LiSa 77 zSz SousS

68 shLVf OLOVO 78 SvF Safe

69 ShlRts Shar 79 SzRts SyR

70 SzNm Sani 80 vFNm FeN

Exercises

1. Perform successively the psychotechnical exercises “Fingers”, “Breathing”, “Warmth”, “Focusing”, “Letters”, “Memory Activation”, “Mental Drawing”, “Image Manipulation”, “Image Transformation”, “Image Rotation” , “Meaningless Monologue”, “Thematic Monologue”.

2. Recode the numbers out loud into fixed figurative codes (the table contains numbers from 01 to 60).

36 11 43 03 18 30 23 07 47 33

53 29 22 31 38 02 49 14 20 26

12 44 04 42 13 46 15 32 39 55

28 54 35 21 01 19 06 24 48 52

37 05 10 50 16 51 40 56 59 37

45 27 41 17 34 09 58 25 60 08

3. Remember 10 words using the “Chain” technique. In each image, select 3 sub-images. For each sub-image, remember a three-digit number.

TAXI STALL MAN CROW LANTERN THERMOS DOOR STOOL CHAMOMILE CASSETTE

246 532 863 702 392 776 027 352 729

809 298 563 289 567 393 539 377 726

620 363 280 613 292 603 726 289 546

4. Remember the sequence of words using the return technique.

MILK SPARROW STICKER FORK APPLE STRAP RING LIGHT BULB STAR WATCH BALLS ATHLETE BRUSH CATERPILLAR NOODLES CLOVE ARROW CLIPPERS CAMPFLY CUP POTATO HORSE STRING COINS

5. Memorize 10 words using the “Chain” technique. For this chain of supporting images, memorize 30 two-digit numbers using the image splitting technique. Memorize three numbers per image. Sequence of numbers in each group in in this case doesn't matter.

ALARM CLOCK FRIDGE PHONE PERSON DESK CAR SPEAKER DRILL VCR CALCULATOR

20-07-21 12-26-03 24-15-25 02-27-11 10-09-01

04 30 14 13 17 16 19 22 05 06 29 18 08 23 28

6. Remember the formula for gas pressure.

p=(m:M)(RT:V)

p - gas pressure

m - gas mass

M - molar mass

R - universal gas constant

T - temperature in Kelvin

7. Remember the sequence of jokes using the information compression method.

The Scotsman is reading a book. From time to time he turns off the light briefly and then turns it on again.

What are you doing? - asks the wife.

You can turn pages even in the dark.

In the office, the director says to the secretary:

Helen, go see why Mr. Harris is yelling like that.

Monsieur, he is speaking to Australia.

Can't he use the phone for this?

What's the best way to teach a girl to swim?

You gently put your left arm around her waist, then you take her left hand and hold it tightly, and then...

You idiot, we're talking about my sister!

You should have said so from the start! Push her off the bridge into the water!

Two hippopotamuses are dancing.

Do you love me? - asks the hippopotamus.

Certainly! I'm dancing all evening today just with you!

This is not proof yet.

Not proof? And you should look at yourself from the outside!

The director asks the secretary:

Are you busy on Sunday?

No, Mr. Director, I’m free, she replies, blushing.

Then try not to be late for work on Monday.

Erhard Jacobsen came to see a psychiatrist.

“I know from the papers who you are,” said the doctor, “and what you do.” But in order to begin serious treatment, I need to know who you really are. I want you to tell me completely frankly about your life - start from the very beginning.

Erhard cleared his throat and began:

So, first I created Heaven and Earth.

A man enters the doctor's office, his hands shaking.

Do you drink a lot? asks the doctor.

Not good. I spill more.

A customer comes out of the pharmacy door. Suddenly the pharmacist runs out after him and shouts:

Sir! By mistake, we gave you potassium cyanide instead of calcium chloride. Please pay twenty cents extra to the cash register.

Pastor to artist:

Are you crazy? Where have you seen angels in boots?

Where have you seen angels without shoes?

One young gentleman wished his parents a Happy New Year.

And they kept me for the second year.

Homework

1．Memorize the fixed codes of two-digit numbers (61 to 80). Repeat and consolidate previous numbers in your memory.

2. Convert numbers into figurative codes. Ensure that transcoding occurs without delay.

13 56 68 33 02 42 09 29 11 57

19 41 26 58 77 18 44 48 36 72

61 05 75 32 12 37 04 51 76 35

20 55 01 38 67 10 31 17 22 50

06 14 59 78 03 43 08 45 28 64

27 39 69 25 53 23 16 71 66 73

62 60 80 74 79 46 65 30 49 52

40 07 54 15 47 24 21 34 70 63

3. Remember the words strictly by their serial numbers.

1. NUMBER 2. SCREEN 3. MEETING 4. EXIT

5. WARRANTY 6. KEYBOARD 7. ELECTRON 8. UNIVERSE

9. THE WAY 10. GOOD 11. SERVICE 12. PEACE

13. UNLOADING 14. COMPUTER 15. FOUNDATION 16. PRINCIPLE

17. SOUND 18. PROBLEM 19. KICK 20. COUNT

21. AMERICA 22. EFFECT 23. BOLT 24. COPPER

25. MAIL 26. BIBLE 27. BASE 28. ABSTRACT

33. TELEVISION 34. FISHING ROD 35. LABORATORY TECHNICIAN 36. BASE

37. PERCENTAGE 38. CRITICISM 39. GRAPHICS 40. NEWS

41. LOCALITY 42. COMMISSION 43. CORNER 44. NEWSPAPER

4. Remember the sequence of jokes.

A man reads in the newspaper that in Los Angeles, one person gets hit by a car every hour.

God, he sighs, the poor fellow is unlucky.

When Mark Twain received an invitation to the funeral of a senator, he said:

I refused to attend this man's funeral, but sent a polite letter in which I wrote that I warmly welcomed the event.

Sorry, but I think I saw your face somewhere else.

This can't be true. I always wear my face in the same place.

A young man comes to a rich industrialist whose daughter he wants to marry. Industrialist says:

Young man, I have made inquiries about your past and I must say...

The young man interrupts him:

I also made inquiries about your past and I must tell you...

Okay, let's talk about something else.

Mom, the mouse jumped into the milk can!

Did you pull it out?

No, but I threw the cat in there!

Quarrel in a young family.

Yes, it turns out you are just an egoist. My wife, my apartment, my salary. Mine, mine... Nothing is yours, There is only ours. You remembered? By the way, what are you looking for in the closet?

“Our trousers,” the husband answers.

The Southern Pacific Express was speeding along the borders of one of the largest cattle ranches in Texas. One of the passengers peers intently at the huge herds grazing along the road. When the train finally passed the ranch, he turned to his neighbor and remarked:

Quite a herd on this ranch. I counted 11,420 heads. The neighbor stared at him in amazement.

Simply incomprehensible! - he announced. By the way, I am the owner of this ranch and I know for sure that I have exactly 11,420 head of cattle. For God's sake, how did you manage to count them when our train is doing 60 miles an hour?

“Oh, it’s quite simple if you know the system,” answered the mathematician. All you need to do is count your legs and divide by four.

Aunt Vlasta, don’t you know how to eat yourself?

Where did you get this from, Pepichek?

When you announced your arrival, dad told mom: “We’ll have to feed your aunt again for a whole week!”

Good evening! I want to say that your daughter agrees to be my wife!

It's your own fault! Why did you have to come to visit us every evening?

5. Memorize formulas using formula memorization techniques.

SPEED OF ORDERED MOTION OF ELECTRONS IN A CONDUCTOR

u = I: (enS)

u is the speed of ordered movement of electrons in a conductor

I - current strength

e - electron charge modulus

n - number of electrons

S - cross-sectional area of the conductor

UNIFORM CIRCULAR MOVEMENT

v = 2πnR

v - speed module

t - circulation frequency

R - radius

Combinatorics is a branch of mathematics devoted to solving problems of choosing and arranging elements of a certain set in accordance with given rules. Combinatorics studies combinations and permutations of objects, the arrangement of elements that have specified properties. A common question in combinatorial problems is: in how many ways….

Combinatorial problems also include problems of constructing magic squares, decoding and encoding problems.

The birth of combinatorics as a branch of mathematics is associated with the works of the great 17th century French mathematicians Blaise Pascal (1623–1662) and Pierre Fermat (1601–1665) on the theory of gambling. These works contained principles for determining the number of combinations of elements of a finite set. Since the 50s of the 20th century, interest in combinatorics has been revived due to the rapid development of cybernetics.

The basic rules of combinatorics are sum rule And rule works.

Sum Rule

If some element A can be selected n ways, and element B can be selected m ways, then the choice “either A or B” can be made n+ m ways.

For example, If there are 5 apples and 6 pears on a plate, then one fruit can be chosen in 5 + 6 = 11 ways.

Product rule

If element A can be selected n ways, and element B can be selected m ways, then a pair A and B can be selected n m ways.

For example, if there are 2 different envelopes and 3 different brands, then you can choose an envelope and a stamp in 6 ways (2 3 = 6).

The product rule is also true when considering elements of several sets.

For example, if there are 2 different envelopes, 3 different stamps and 4 different postcards, then you can choose the envelope, stamp and postcard in 24 ways (2 3 4 = 24).

The product of all natural numbers from 1 to n inclusive is called n - factorial and is denoted by the symbol n!

n! = 1 2 3 4 … n.

For example, 5! = 1 2 3 4 5 = 120.

For example, if there are 3 balls - red, blue and green, then you can put them in a row in 6 ways (3 2 1 = 3! = 6).

Sometimes a combinatorial problem is solved by constructing tree possible options.

For example, let's solve the previous problem about 3 balls by building a tree.

Workshop on solving problems in combinatorics.

CHALLENGES and solutions

1. There are 6 apples, 5 pears and 4 plums in a vase. How many options are there for choosing one fruit?

Answer: 15 options.

2. How many options are there for purchasing one rose if they sell 3 scarlet, 2 scarlet and 4 yellow roses?

Answer: 9 options.

3. Five roads lead from city A to city B, and three roads lead from city B to city C. How many paths through B lead from A to C?

Answer: 15 ways.

4. In how many ways can you make a pair of one vowel and one consonant of the word “scarf”?

vowels: a, o – 2 pcs.
consonants: p, l, t, k – 4 pcs.

Answer: 8 ways.

5. How many dance couples can be made from 8 boys and 6 girls?

Answer: 48 pairs.

6. There are 4 first courses and 7 second courses in the dining room. How many different two-course lunch options can you order?

Answer: 28 options.

7. How many different two-digit numbers can be made using the numbers 1, 4 and 7 if the numbers can be repeated?

1 digit – 3 ways
2 digit – 3 ways
3 digit – 3 ways

Answer: 9 different two-digit numbers.

8. How many different three-digit numbers can be made using the numbers 3 and 5, if the numbers can be repeated?

1 digit – 2 ways
2nd digit – 2 ways
3rd digit – 2 ways

Answer: 8 different numbers.

9. How many different two-digit numbers can be made from the digits 0, 1, 2, 3, if the digits can be repeated?

1 digit – 3 ways
2 digit – 4 ways

Answer: 12 different numbers.

10. How many three-digit numbers are there in which all digits are even?

Even numbers – 0, 2, 4, 6, 8.

1 digit – 4 ways
2 digit – 5 ways
3 digit – 5 ways

Answer: There are 100 numbers.

11. How many even three-digit numbers are there?

1 digit – 9 ways (1, 2, 3, 4, 5, 6, 7, 8, 9)
2nd digit – 10 ways (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
3rd digit – 5 ways (0, 2, 4, 6, 8)

9 10 5 = 450

Answer: There are 450 numbers.

12. How many different three-digit numbers can be made from three different digits 4, 5, 6?

1 digit – 3 ways
2nd digit – 2 ways
3rd digit – 1st way

Answer: 6 different numbers.

13. In how many ways can you designate the vertices of a triangle using the letters A, B, C, D?

1 top – 4 ways
2nd top – 3 ways
3rd top – 2 ways

Answer: 24 ways.

14. How many different three-digit numbers can be made from the digits 1, 2, 3, 4, 5, provided that not a single digit is repeated?

1 digit – 5 ways
2 digit – 4 ways
3 digit – 3 ways

Answer: 60 different numbers.

15. How many different three-digit numbers less than 400 can be made from the digits 1, 3, 5, 7, 9, if any of these digits can be used only once?

1 digit – 2 ways
2 digit – 4 ways
3 digit – 3 ways

Answer: 24 different numbers.

16. In how many ways can a flag be made, consisting of three horizontal stripes of different colors, if there is material of six colors?

1 lane – 6 ways
2 lane – 5 ways
3 lane – 4 ways

Answer: 120 ways.

17. 8 people are selected from the class who have top scores on the run. In how many ways can they form a team of three people to participate in a relay race?

1 person – 8 ways
2 people – 7 ways
3 people – 6 ways

Answer: 336 ways.

18. On Thursday in the first grade there should be four lessons: writing, reading, mathematics and physical education. How many different schedule options can you create for this day?

1 lesson – 4 ways
Lesson 2 – 3 ways
Lesson 3 – 2 ways
Lesson 4 – method 1

4 3 2 1 = 24

Answer: 24 options.

19. In the fifth grade, 8 subjects are studied. How many different schedule options can be created for Monday, if there should be 5 lessons on this day and all the lessons are different?

1 lesson – 8 options
Lesson 2 – 7 options
Lesson 3 – 6 options
Lesson 4 – 5 options
Lesson 5 – 4 options

8 7 6 5 4 = 6720

Answer: 6720 options.

20. The code for the safe is made up of five different numbers. How many different options for creating a cipher?

1 digit – 5 ways
2 digit – 4 ways
3 digit – 3 ways
4 digit – 2 ways
5 digit – 1 way

5 4 3 2 1 = 120

Answer: 120 options.

21. In how many ways can 6 people be seated at a table with 6 cutlery?

6 5 4 3 2 1 = 720

Answer: 720 ways.

22. How many seven-digit phone numbers can be created if you exclude numbers starting with zero and 9?

1 digit – 8 ways
2 digit – 10 ways
3 digit – 10 ways
4 digit – 10 ways
5 digit – 10 ways
6 digit – 10 ways
7 digit – 10 ways

8 10 10 10 10 10 10 = 8.000.000

Answer: 8,000,000 options.

23. The telephone exchange serves subscribers whose telephone numbers consist of 7 digits and begin with 394. How many subscribers is this station designed for?

Phone number 394

10 10 10 10 = 10.000

Answer: 10,000 subscribers.

24. There are 6 pairs of gloves of different sizes. In how many ways can one choose from them one glove for the left hand and one glove for the right hand so that these gloves are of different sizes?

Left gloves - 6 ways
Right gloves - 5 ways (6th glove is the same size as the left one)

Answer: 30 ways.

25. The numbers 1, 2, 3, 4, 5 make up five-digit numbers in which all the digits are different. How many such even numbers are there?

5th digit – 2 ways (two even digits)
4 digit – 4 ways
3 digit – 3 ways
2nd digit – 2 ways
1 digit – 1 way

2 4 3 2 1 = 48

Answer: 48 even numbers.

26. How many four-digit numbers are there, made up of odd digits and divisible by 5?

Odd numbers – 1, 3, 5, 7, 9.
Of these, they are divided into 5 – 5.

4 digit – 1 way (digit 5)
3 digit – 4 ways
2 digit – 3 ways
1 digit – 2 ways

1 4 3 2 = 24

Answer: 24th.

27. How many five-digit numbers are there in which the third digit is 7 and the last digit is even?

1 digit – 9 ways (all except 0)
2 digit – 10 ways
3 digit – 1 way (digit 7)
4 digit – 10 ways
5 digit – 5 ways (0, 2, 4, 6, 8)

9 10 1 10 5 = 4500

Answer: 4500 numbers.

28. How many six-digit numbers are there in which the second digit is 2, the fourth is 4, the sixth is 6, and all the rest are odd?

1 digit – 5 options (from 1, 3, 5, 7, 9)
2 digit – 1 option (digit 2)
3rd digit – 5 options
4 digit – 1 option (digit 4)
5 digit – 5 options
6 digit – 1 option (digit 6)

5 1 5 1 5 1 = 125

Answer: 125 numbers.

29.How many different numbers less than a million can be written using the numbers 8 and 9?

Single digits – 2
Double digits – 2 2 = 4
Three-digit numbers – 2 2 2 = 8
Four-digit numbers – 2 2 2 2 =16
Five-digit – 2 2 2 2 2 = 32
Six-digit numbers – 2 2 2 2 2 2 = 64

Total: 2 + 4 + 8 + 16 + 32 + 64 = 126

Answer: 126 numbers.

30.V football team 11 people. You need to choose a captain and his deputy. In how many ways can this be done?

Captain - 11 ways
Deputy - 10 ways

Answer: 110 ways.

31.There are 30 people in the class. In how many ways can you choose the headman and the person responsible for travel tickets?

Headman - 30 ways
Answer. for tickets - 29 ways

Answer: 870 ways.

32. 12 boys, 10 girls and 2 teachers are participating in the hike. How many options for groups of three people on duty (1 boy, 1 girl, 1 teacher) can be formed?

12 10 2 = 240

Answer: 240 ways.

33. How many combinations of four letters of the Russian alphabet (there are only 33 letters in the alphabet) can be made, provided that 2 adjacent letters are different?

Mnemonics [Memorization based on visual thinking] Ziganov Marat Aleksandrovich

19. Fixed figurative codes of two-digit numbers Association list method (AS-100)

19. Fixed figurative codes of two-digit numbers

Associated List Method (AS-100)

WITH general concept figurative codes you'll meet later. For now it is enough to understand: In order for numerical information to be remembered quickly enough, you need to memorize one hundred images. Each image is strictly assigned to its own number (from 00 to 99). As soon as you remember this list, you will immediately be able to remember large volumes of any digital information, for example, dozens of telephone numbers, without errors.

Coding of two-digit numbers is carried out through an alphanumeric code (BCC).

12 GZh DT Gzh dT Guitar image of a guitar

35 KX PB Kx pB CuB cube image

The numbers 01. 02. 03... 09 in the number series are encoded into images as 1. 2. 3... 9. When recalled, a zero is added to them on the left.

05 - PB PB Wallpaper image

06 - SHL shL yuLa image

07 - NW NW oSa image

Please remember separately: 0 - number; 00 - barrels.

The list should be memorized gradually (10-20 images at a time) in the process of learning other memorization techniques.

List of fixed figurative codes

two-digit numbers from 01 to 20

1. GZh EZH 11 GzhGzh GaGarin

2. Dt YaD 12 GZhT Guitar

3. kX uKho 13 GzhKh Nut

4. Chch Tea 14 g ZhChok ZhuChok

5. pb wallpaper 15 gzpb lips

6. shL YuLa 16 Gzhl Gouache

7. Sz oSa 17 GzhSz GuS

8. Vf iVa 18 GzhVf GVozd

9. rc egg 19 gjrc girya

10. GzhNm FIRE 20 DtnM HOUSE

author

3.15 Figurative codes and high-speed memorization Elements of any information messages must be converted into simple and easy-to-memorize visual images before memorizing. The process of converting elements of information messages into visual images

From the book Mnemonics Textbook author Kozarenko Vladimir Alekseevich

4.14 Figurative codes of three-digit numbers (000-999) Please note that in figurative codes of three-digit numbers, coding starts from zero again: 01 - gZh - Zh - eZh,001 - nM Nm gZh - MNZH - MaNZhet02 - Dt - D - yD,002 - nM Nm dT - MNT - MonetA In the figurative codes of three-digit numbers, everything is encoded into letters

From the book Mnemonics Textbook author Kozarenko Vladimir Alekseevich

4.15 Figurative codes for the names of months Figurative codes for the names of months are selected arbitrarily using symbolization techniques or linking to well-known information. These figurative codes are used to remember the names of months in exact dates, as well as in some other

From the book Mnemonics Textbook author Kozarenko Vladimir Alekseevich

4.16 Figurative codes for days of the week Figurative codes for days of the week are convenient to use for remembering various schedules. For example: lesson schedules at school, college, train schedules. These figurative codes can be used to remember your own affairs on

From the book Mnemonics Textbook author Kozarenko Vladimir Alekseevich

4.17 Figurative codes of letters of the alphabet Figurative codes of letters of the alphabet can be composed arbitrarily. The main thing is that they do not intersect with other figurative codes. Thus, the figurative codes you used to encode the letters of the Russian alphabet should not be used when

From the book Mnemonics Textbook author Kozarenko Vladimir Alekseevich

4.18 Phonetic figurative codes Phonetic figurative codes are used to quickly and very accurately memorize the pronunciation of new foreign words. Phonetic figurative codes can overlap with other figurative codes, since memorization with their help is

From the book Mnemonics Textbook author Kozarenko Vladimir Alekseevich

4.19 Other figurative codes Figurative codes are the language of mnemonics. Without knowledge of the system of figurative codes, memorization will turn into torture. Each time it will take a painfully long time to select images to match the memorized elements of information. Pre-learned figurative codes make

author

26. Figurative codes In mnemonics, a variety of figurative codes are widely used. A figurative code is a visual image rigidly attached to any element of information (for example, a two-digit number). The figurative code is learned so that its recall is