Number pyramids. Number pyramid Bulls and cows

Test work based on the results of the first half of the year (grade 7)

Option I _____________________________________________________

1. Fill in the blanks in the “pyramid” of interpersonal relationships: Love, Friendship, ____________, Fellowship, ____________________

2. Relations related to compliance with any formalities or rules established by an official:

a) official b) personal c) work d) home

3. Personal relationships include (underline): a party of friends, negotiations for a job, a picnic trip, a camping trip, a conversation between a school principal and a student’s parents, a family quarrel, a meeting with the head of a foreign state, congratulations on a brother’s birthday, congratulations on the anniversary of a distinguished person, a friendly conversation between peers, a meeting at the enterprise .

4. Establish a correspondence between examples of social groups and their types:

5. From judgments A and B it is true:

A. Communication is a necessary condition for the full existence of a person; he cannot live without communication with other people

B. A person can do without communication; it is not a necessary condition for his existence.

6. From judgments A and B it is true: 1) only A 2) only B 3) both A and B 4) neither A nor B

A. Conflict is a clash of opposing goals, interests, views, opinions

B. The role of conflicts in the lives of people and society can be both negative and positive

: The guys quarreled over watching a TV show. Oleg wanted to watch football, and Igor wanted to watch a feature film. Igor was the older brother and Oleg had to give in.

A) submission, b) compromise, c) interruption of conflicting actions, d) integration

8. It is known that communication can be verbal and non-verbal. Select examples of verbal communication from the list (underline): gaze, story, facial expressions, gestures, posture, gait, judgments, cry, song, flowers, gift, compliment, threat, dance.

9. It is known that conflicts can be constructive and unconstructive. Finish the sentence: If the parties to the conflict do not go beyond business arguments and moral relations, then we have an example of a ____________________ conflict.

10. Relate

1Rights necessary to protect life, freedom, and personal dignity

2.Rights and freedoms that are designed to ensure citizen participation in the management of state affairs

3. Rights and freedoms that enable a citizen to achieve well-being and satisfy his needs

4. Rights and freedoms that are designed to provide a citizen with a decent life

5. Rights and freedoms that are associated with a citizen’s access to spiritual and material values created by humanity

A) Political

B) Economic

B) Social

D) Civil (personal)

D) Cultural

11. On what principle is the series formed?

A) Freedom of thought, speech, press, right to information, freedom of association, freedom of assembly, rallies, demonstrations, the right to vote and be elected, the right to participate in a referendum, the right to appeal to the state. bodies, equal right of access to any positions.

IN)

A) Citizens of the Russian Federation from 18 to 27 years of age who are or are required to be registered with the military are called up for military service

B) The term of military service in the Russian Federation is 24 months

D) A citizen must register for military service at his place of residence at the military commissariat in the year he reaches 14 years of age

A) Compliance with the rules for students __________________________

B) Strict observance of laws and strict fulfillment of the requirements of the Military Oath. Military regulations, orders of higher commanders _______________

C) Accurate execution of administration orders, rational use of working time, compliance with labor regulations __________________________

15.

Defense of the Fatherland is the duty and __________________ of a citizen of the Russian Federation. A feeling of hostility, dislike. A collection of several laws combined into one law. Local military administration body in Russia, which is in charge of registering youth subject to conscription for military service. Mutual business or friendly relations between people.

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Test work based on the results of the first half of the year (grade 7)

Option II_________________________________________________

1. Fill in gaps in the “pyramid” of interpersonal relationships: Love, Friendship, _____________, ____________________, Acquaintance

2. Relations related to compliance with any formalities, rules established by the administration or any official

A) personal b) family c) official d) friendly

3. Official (business) relations include (underline): a party of friends, negotiations for a job, a picnic trip, a camping trip, a conversation between a school principal and a student’s parents, a family quarrel, a meeting with the head of a foreign state, congratulations on a brother’s birthday, congratulations on the anniversary of a distinguished person, a friendly conversation between peers, a meeting at the enterprise .

4. Establish a correspondence between examples of social groups and their types:

5. From judgments A and B it is true: 1) only A 2) only B 3) both A and B 4) neither A nor B

A. Even the most protracted conflict ends sooner or later

B. Often a careless word or insufficient attention to a person provokes a conflict

6. From judgments A and B it is true: 1) only A 2) only B 3) both A and B 4) neither A nor B

A. The desire to communicate appears in a person at school age

B, Communication is one of the most important needs of the individual.

7. Determine how to resolve the conflict: The guys quarreled over watching a TV show. Oleg wanted to watch football, and Igor wanted to watch a feature film. Igor proposed the following option: today Oleg chooses the right to watch the program, and tomorrow Igor will decide which film to watch. Oleg agreed with this decision.

A) submission, b) compromise, c) interruption of conflicting actions, e) integration

8. It is known that communication can be verbal and non-verbal. Select examples of non-verbal communication from the list (underline): gaze, story, facial expressions, gestures, posture, gait, judgments, shouting, song, flowers, gift, compliment, threat, dance.

9. It is known that conflicts can be constructive and unconstructive. Complete the sentence: If one of the parties to the conflict resorts to morally condemnable actions (eg: insults), then we have an example of a _________________________ conflict

10. Relate

1Rights and freedoms that are designed to provide a citizen with a decent life

2. Rights and freedoms that are associated with a citizen’s access to spiritual and material values created by humanity

3. Rights and freedoms that are designed to ensure citizen participation in the management of state affairs

4. Rights necessary to protect life, freedom, and personal dignity

5. Rights and freedoms that enable a citizen to achieve well-being and satisfy his needs

A) Political

B) Economic

B) Social

D) Civil (personal)

D) Cultural

11.On what principle is the series formed:

A) Right to life, right to protection of honor and dignity, right to freedom and personal integrity, freedom of movement, choice of place of residence, right to privacy, personal and family secrets, freedom of conscience and religion, right to inviolability of home_____________________________________________

B) Comply with laws; pay taxes; defend the Fatherland, perform military service; protect historical and cultural monuments; preserve nature and the environment _____________________________________

V) The right to work, the right to rest, the right to social security, the right to health care and medical care, the right to education, the right to housing, the right to a favorable (healthy) environment, the right to state protection of family, motherhood and childhood. _____________________________________________________

12. Correlate the characteristics of human rights and their definitions:

13. Check the correct statements:

A) Citizens of the Russian Federation from 18 to 60 years of age who are or are required to be registered with the military are called up for military service

B) The term of military service in the Russian Federation is 12 months

C) A serviceman entering military service for the first time is taken the Military Oath in front of the State Flag of the Russian Federation and the Battle Banner of the military unit

D) A citizen must register for military service at his place of residence at the military commissariat in the year he reaches 18 years of age

D) After taking the military oath, a serviceman may be involved in combat missions, weapons and military equipment may be assigned to him

14.What discipline are we talking about:

A) Strict and exact observance by all military personnel of the order and rules established by laws and military regulations __________________________

B) Strict adherence to established procedures in production _______________

C) Compliance with the rules for students ________________________________________________

14. Solve the crossword puzzle. Make up a sentence with the keyword.

1. Internal disposition, a person’s stable approving attitude towards other people.

2. A solemn promise (oath) of a citizen upon his entry into the ranks of the armed forces

3. A measure of influence applied to violators or a method of approval, encouragement, support.

4. A document by which conscripts are summoned to the military commissariat to clarify issues of military registration (citizen credentials) and carry out activities related to the preparation and conduct of conscription of citizens for military service

5. A certain order of people’s behavior that meets the established norms of law and morality in society or the requirements of any organization

Make a sentence with a keyword

In this issue we will look at the classic problem known as the “Golden Mountain”. It was implemented at CheckiO in this task.

Imagine a triangle made up of numbers. One number is located at the top. Below are two numbers, then three, and so on until the bottom edge. You start at the top and need to work your way down to the bottom of the triangle. For each move, you can go down one level and choose between two numbers below the current position. As you move, you “collect” and add up the numbers you pass. Your goal is to find the maximum amount that can be obtained from various routes.

Let's consider various solution methods.

Recursion

The first thing that comes to mind is to use recursion and calculate all the paths from the top. When we go down one level, all the available numbers below form a new smaller triangle, and we can run our function for a new subset and so on until we reach the bottom.

Def golden_pyramid(triangle, row=0, column=0, total=0): global count count += 1 if row == len(triangle) - 1: return total + triangle return max(golden_pyramid(triangle, row + 1, column, total + triangle), golden_pyramid(triangle, row + 1, column + 1, total + triangle))

As we can see, at the first level we will run our function twice, then 4, 8, 16 times and so on. As a result, we will get the complexity of the algorithm 2 N and, for example, for a 100-level pyramid we will need about ≈10 30 function calls. A bit much.

Dynamic programming

What if we try to use the principle of dynamic programming and break our problem into many small subtasks, the results of which we then accumulate. Try looking at the triangle upside down. And now to the second level (that is, the penultimate one from the base). For each cell, we can decide what the best choice will be in our little three-element triangles. We select the best one, sum it with the cell in question and write down the result. Thus, we got our triangle, but one level lower. We repeat this operation again and again. As a result, we need (N-1)+(N-2)+…2+1 operations and the complexity of the algorithm is N 2 .

Def golden_pyramid_d(triangle): tr = for row in triangle] # copy for i in range(len(tr) - 2, -1, -1): for j in range(i + 1): tr[i][j ] += max(tr[j], tr) return tr

CheckiO player decisions

User gyahun_dash wrote an interesting implementation of the DP method described above in his "DP" solution. He used reduce to iterate over pairs of strings and map to process each of them.

From functools import reduce def sum_triangle(top, left, right): return top + max(left, right) def integrate(lowerline, upperline): return list(map(sum_triangle, upperline, lowerline, lowerline)) def count_gold(pyramid) : return reduce(integrate, reversed(pyramid)).pop()

Player evoynov used binary numbers to iterate over all possible routes, represented as a sequence of 1s and 0s in his solution "Binaries". And this is a clear example of the complexity of the algorithm with recursion and enumeration of all routes.

Def count_gold(p): path = 1<< len(p) res = 0 while bin(path).count("1") != len(p) + 1: s = ind = 0 for row in range(len(p)): ind += 1 if row >0 and bin(path) == "1" else 0 s += p res = max(res, s) path += 1 return res

And so that it doesn’t get boring, let’s look at an easy mind-bender from user nickie and his one-liner “Functional DP”, which only formally consists of two lines. Of course, this is a solution from the “Creative” category. I don't think the author uses this in combat code. But just for fun, why not.

Ount_gold=lambda p:__import__("functools").reduce(lambda D,r:,D) for j,x in enumerate(r)],p[-2::-1],list(p[-1] ))

That's all for today. Share your ideas and thoughts.

On astrological symbols. Some of them are quite complex and require certain skills, for example, predictions using the positions of the planets in the sky, some are even dangerous, such as predictions associated with. There are also very simple fortune telling, such as fortune telling on a coin. The number pyramid is a fairly simple and safe method of fortune telling, and also requires very little time.

Fortune telling method

It is necessary to ask the question correctly, so that the second word is always “whether”. For example, “will Natalya Ivanova marry Semyon Semenov?”

If the number of letters in a word exceeds 9, then you need to add up the numbers in the number and write down the result. For example, the number of letters in a word is 12, 1 is added to 2, we get 3, which is written in a row.

Next, you need to add the first and second numbers, and write the result under them. 6 plus 2 gives 8. Then the second and third numbers are added, and the result is written under them. 2 plus 7 equals 9. The same must be done with the third and fourth numbers, with the fourth and fifth, etc.

If the sum of the numbers exceeds 9, then you need to add the numbers that make up the number and write down the result. As in the example, 7 plus 7 gives 14, 14 is more than 9, so you need to add the numbers 1 and 4, and the resulting result 5 is written under 7 and 7.

This procedure must be done with all the numbers in the first row until you get a new row of numbers below it. The number of numbers in the second row should be one less than in the first.

Now you need to do the same procedure with the numbers in the second row, writing the results below. The first number of the second row is added to the second number of the second row and the result is written below them, forming the first number of the third row.

This results in a third row, the number of digits in which will be one less than in the previous row.

This addition must be carried out until there is one single digit in the last row.

This figure will be the answer to the question.

Since all the rows written under each other form an inverted pyramid of numbers, at the top of which is the answer, fortune telling is therefore called.

Interpretations of the answer

In this fortune-telling, only nine possible answers are possible, therefore, as in many other fortune-telling, it is necessary to resort to the help of intuition to make the answer more succinct. Below is a breakdown of the answers based on the numbers received at the top of the pyramid.

1 – you know yourself;

2 – yes;

3 – no;

4 – of course;

5 – possible;

6 – there will be difficulties;

7 – hope and wait;

8 – yes, but not now;

9 – not now.

In order for fortune telling to occur with the greatest accuracy, you need to ask the question correctly, entering into it as much data as possible that is known to the fortuneteller. Also, in a question about yourself, the fortuneteller should write his last name, first name and patronymic instead of “I”.

Goals:D

didactic:

ensure the assimilation of the concept of a pyramid and its elements;
recognize a pyramid among other three-dimensional bodies;
introduce some historical and practical information.

developing:

develop memory, thinking and speech of students, the ability to analyze and draw conclusions;
develop spatial imagination.

educational:

develop the ability to work in a team (groups, pairs);
cultivate diligence, diligence and responsibility.

Everything in the world is afraid of time,
And time is afraid of pyramids

Arabic proverb

DURING THE CLASSES

1. Organizational moment: Greeting.

The lesson is accompanied by a presentation. Annex 1

We marvel at flowers, forests and skies,
Everything that nature has done
Everything I did myself.
Do you believe in miracles, guys? (Yes)
How many miracles are there in the world? (7)
Now let's take a trip
Into the world of these ancient wonders.
(Film “Seven Wonders of the World”) Slide 2.

What wonder of the world is connected with mathematics? (Pyramid)

What will we talk about in today's lesson? (About the pyramid)

Find it among your figures

And write this word down in your notebook.

Today in the lesson we will get acquainted with the concept of a pyramid and its elements, we will learn to depict a pyramid in a notebook and recognize it among other bodies.

Pyramid is a word of Greek origin meaning “Fire”. Why? (Students' answers)

But we will look at the concept of a pyramid from a mathematical point of view.

There are different figures
We can’t count them all
Look at the figures
And quickly determine...

What groups can these figures be divided into? (Flat and volumetric)

What, in one word, can you call the figures of each group? (Flat - polygons, volumetric - polyhedra)

Feel free to pick up the pyramid and let’s get down to business
We will study the figure thoroughly,
And every element of it is thorough.

Try to define a pyramid. (Students' answers).

Definition (given by the teacher after the students) : A pyramid is a polyhedron consisting of a polygon and triangles. The polygon is the base, the triangles are the side faces.

The segments along which the faces intersect are called edges; in a pyramid, there are lateral edges and base edges. The points where the edges intersect are called vertices.

A pyramid is called by the number of sides of its base. If there is a triangle at the base, it is triangular. Give the following pyramids a name. (Quadragonal, pentagonal, hexagonal)

Primary consolidation of the studied material.

Take green sheets and pyramids. Option 1 – triangular, 2 – quadrangular. Explore your pyramid and fill out the table based on the results (children are given a blank table).

According to the table, fill in the gaps in the text.

The number of vertices of a pyramid is _____ more than the number of vertices at its base.

The number of side faces _____ the number of sides of the base.

Fill out the table.

Slide check.

How many correct answers are there, rate yourself that way. Visual check. Raise your hands, those who received a “5”, then those who received a “4”. Well done.

Based on the research results, fill in the gaps in the text next to the table.

Now let’s check the answers written in the text.

The number of vertices of a pyramid is one more than the number of vertices at its base.

The number of side faces is equal to the number of sides of the base.

You had different pyramids, but the answers were the same. What hypothesis can we put forward for any pyramid? (The number of vertices of any pyramid is one greater than the number of vertices at its base, and the number of side faces is equal to the number of sides of the base). Our hypothesis will become a statement in 10th grade geometry lessons.

And the Spasskaya Tower on Red Square
It is very familiar to both children and adults.
Look at the tower - it looks ordinary,
What's on top of it? Pyramid!

In architecture, the roofs of houses are often built in the form of pyramids.

Among the bodies depicted, choose those that are pyramids. (1, 3, 4, 7, (5, 9))

What word do you think the word “sweep” comes from? (Expand, expand)

Right! If the pyramid is cut along the side edges and unfolded onto a plane, you will get... (triangle).

The triangular pyramid has several types of developments. One of them is a quadrilateral (parallelogram).

Here is the pyramid layout
It's not all that complicated at first glance
Look at the scan
Base, three sides
If you put them together right
You can imagine the general view.

Now we will weave a pyramid from two developments (we use the textbook Sharygin I.F., Erganzhieva L.N. Visual geometry: grades 5–6):

In front of you are two scans, one white, the other red.

On one side there is a solid line. Take the white one, bend it along the lines so that the lines are on the outside, that is, you can see them.

Then we work with the red one: we bend along the lines, but the lines should be inside, that is, you don’t see them.

Both white and red have marks. Connect them so that the white one is on top.

From the red one, assemble a pyramid. Wrap the white one around the red one, and place the last triangle in the gap between the two red ones. The result is a triangular pyramid. It is often called a tetrahedron. Write this word in your notebook.

Physical pause.

We worked hard, let's have a good rest
Here's a minute for a game or exercise.
We're counting one, two, three
We stood in order (doing exercises to music).

1. Raise your arms up from the sides, clasp them in a lock and turn your palms towards the ceiling - rock back a maximum of 3 times.

2. Apply pressure to the elbow with the palm of the opposite hand (the hand is parallel to the shoulder girdle) - 3 times.

3. Close your eyes and slowly turn your head from the left shoulder to the right and vice versa 3 times.

We all sat down quietly. And they didn’t hurt each other.

A triangular pyramid is three-dimensional, how can it be depicted on a flat sheet? Now we will learn to draw a triangular pyramid in a notebook. We work step by step.

Step 1. Mark two points on the same line at a distance of 3 cm from each other.

Step 2. Step back the third point from the first planned one 2 cm up and 2 cm to the right.

Step 3. Step back the fourth point from the first planned one 1 cm down and 1 cm to the right.

Step 4. Connect all the obtained points with segments.

Does it look like a pyramid? (Yes). But there is one inaccuracy. How many sides does a triangular pyramid have? (4). What do we see in the drawing? (2). We need to build invisible edges, invisible faces. Invisible edges are usually indicated by a dotted line. See how to connect the dots. So, on a flat sheet of paper, we depicted a three-dimensional figure, a pyramid.

The pyramid can also be found in literature. Poets write poems in the form of a pyramid - a triangle.

This is what Valery Bryusov’s poem “Pyramid-Triangle” looks like.

I
barely
rocking
ropes,
in chenille
without discriminating
blue tones
and sweet head,
I fly in space
winged like a bird,
between the purple bushes!
But in a tempting gaze,
I know it shines, alley, lightning!
And I am happy with her beyond words!

I saw the picture. In this picture
Stands a pyramid in the sandy desert
Everything in the pyramid is extraordinary
There is some kind of mystery and mystery in it.

What famous pyramid is this poem talking about (the Pyramid of Cheops).

The Great Pyramid of Cheops is a fantastic masterpiece of engineering. The weight of the pyramid is more than 6 million tons. The height of the pyramid is about 148 meters, which is equal in millions of kilometers to the distance from the Earth to the Sun.

There is a legend that tells how Thales found the height of the pyramid. He proposed a simple and beautiful solution for this problem. Sticking a long pole vertically into the ground, he said:

When the shadow of this pole has the same length as the pole, the shadow of the pyramid will have the same length as the pyramid. (Demonstration)

The ancient pyramid comes to our aid in completely unexpected areas. Where did you encounter the pyramid? (Students' answers)

The most significant areas of application of the pyramid:

increasing seed yield;

You can conduct experiments with seeds: place them a third of the height of the pyramid in a line oriented “north - south”. Leave the seeds inside the pyramid for a week. Drop them off. The result will immediately affect the first stages of plant development.

duration of storage of products;
health improvement;
energy information protection and much more.

Have any of you been to Egypt? And stood at the pyramid? Do you want one? (Yes).

To imagine the height of the Great Pyramid, we will make a copy of it, reduced by 2000 times. (Practical work, making a pyramid. Appendix 2)

And compare ourselves to her. (Give buckwheat grains to the children, we are buckwheat). Impressive size.

Summarize.

What was discussed in class today? (About the pyramid)
What shape are the side faces of the pyramid? (Triangle)
How many edges come from one vertex? (3)
You need to make a frame model of a triangular pyramid, all edges of which are equal to 7 cm. How many cm of wire will be needed? (6 * 7 = 42 cm)

Homework.

Everything is known around, nevertheless
There is still a lot on earth
Which is sometimes worthy of surprise both yours and mine.

The Egyptian pyramids are a collection of mysteries that not only disturb the imagination and force you to work hard and solve them, but also give rise to new and new mysteries all the time. No wonder the Arabic proverb says: “Everything in the world is afraid of time, and time is afraid of the pyramids.” Scientists have recently discovered that the location of the three largest pyramids at Giza is exactly the same as that of the stars known as Orion's Belt.

Prepare an oral story at home about some secret of the Cheops pyramid.

Let's evaluate our activities in class. Let's turn on the traffic light. Show the result.

I want to end the lesson with these words:

Marvel at the dew, marvel at the flowers,
Be amazed at the elasticity of steel.
Be surprised at what people sometimes
They've stopped being surprised.
Thank you for the lesson. Goodbye.

Number pyramids

Do this pyramid addition as quickly as possible. The principle is simple: in each pyramid, the number in the circle is the sum of the two numbers in the circles below it; your task is to fill in the empty circles to complete the pyramids. Can you complete all three pyramids in less than 60 seconds?

Here's another challenge: imagine these three flat pyramids as three sides of one pyramid with a triangular base. What will be the sum of all the numbers in the second row? What's special about this number?

GYMNASTICS FOR A SMART BRAIN

Remember these 5 names: Germaine McCalla, Augustus Wilson, Rowan Phillips, Randy Green, Armand Sylvester. Connect these names with sensory sensations: speak or sing them, create visual images, associate touches or smells with them. After 1 minute, close the book and try to write them down in the same order.

From the book Ears Waving a Donkey [Modern social programming. 1st edition] author Matveychev Oleg Anatolyevich

From the book Naughty Child of the Biosphere [Conversations about human behavior in the company of birds, animals and children] author Dolnik Viktor Rafaelevich

From the book Pickup. Seduction tutorial author Bogachev Philip Olegovich

From the book 30 most common ways to cheat on the street author Khatskevich Yu G

Exercise 1: Linguistic pyramids To begin with, I’ll tell you what they are - “linguistic pyramids”. Let's start by taking a look around. The first thing my eye fell on was the mug. The mug itself is just a mug, nothing more. However, the mug

From the book Super Brain Trainer by Phillips Charles

The Great Pyramids It is believed that the first financial pyramid was built in the United States in 1919. Its author, Charles Ponti, an Italian emigrant, tried to start a business in America. He opened the Securities Exchange company, which raised funds of various kinds

From the book Change yourself. How to find your unique path to success and happiness by Gebay Jonathan

Number sequences Which of the options presented in the bottom row - A, B, C or D - reproduces the principle of the first three number squares in the top sequence? As you already know from the introduction, brain stimulation promotes the growth of new brain cells.

From the author's book

Numerical Steps Here's another test of spatial sequential logic for developing the visualization skills that are so important for memory function. This time your task is to place the numbers 1 to 9 in a grid so that you can step from one number to the next in order.

From the author's book

Number Ladders The ability to think quickly and be comfortable with numbers, which our Number Ladders puzzle develops, are key attributes for memory function. Your task is to start with the given numbers, and then complete everything sequentially

From the author's book

Number Wheels As you've seen, keeping your memory working at its best requires alertness, focus, and intellectual engagement. The Number Wheels challenge develops clarity of thought and confidence in handling numbers. Yours

From the author's book

Numerical Steps Are you able to work under pressure without compromising accuracy and precision? Start with the top left rectangle and move from one “ramp” to the next as quickly as possible, following the math instructions to get the overall

From the author's book

Problem 10: Number Steps The completed grid should look like the one below. You needed the top right diamond clue to move from 1 to 2, then the diamond below it to move from 2 to 3, etc.

From the author's book

Problem 13. Numerical ladders Easy “ladder” – 9; difficult - 4. I always tell those who have difficulty doing arithmetic in their head: “Practice a little and it will do you good.” It's not that difficult to solve a couple of examples in a collection of puzzles or

From the author's book

Problem 18. Number wheels The missing number is 3. In each wheel, add the values of the white circles, add the values of the black circles and subtract the first sum from the second to get the number in the center. The sum of the white circles in wheel A: 4 + 3 + 2 + 8 = 17. Sum of dark ones: 5 + 6 + 6 + 7 = 24 (24 – 17 = 7).

From the author's book

Problem 19. Number pyramids The completed pyramids are shown below. Did you notice the numbers at their vertices? For an extra memory boost, close the book and see if you can re-draw the completed pyramids. Gymnastics for a smart brain: 28 + 24 + 23 +

From the author's book

Problem 57. Numerical steps The answer is 154, it turns out like this: 257 + 59 (= 316); 25% of 316 = 79; 79 x 3 = 237; 237 – 93 = 144; 144 + 32 = 176; 176? 8 x 5 = 110; 110 + 44 =

From the author's book

Building the Pyramid of Perception Achieving your goals—professional or personal—becomes possible by inspiring a series of successful steps. Figure 1In 1970, one of the greatest psychologists of the 20th century, Abraham Maslow, died, who left a huge