Entertaining arithmetic Perelman Yakov Isidorovich read. Algebra, geometry, physics, puzzles, problems, experiments

Interesting arithmetic.Perelman Ya.I.

L.: Time, 1926.- 192 p.

Available in Russian whole line original and translated collections, pursuing generally the same goal as real book: revive school math introduction to it interesting tasks, entertaining exercises, interesting theoretical and practical information. Those familiar with this literature are well aware that most of these books assiduously draw their material from the same limited fund, accumulated over centuries; hence the close similarity of these works, which develop, with varying detail, almost the same themes. But the traditional inventory of mathematical entertainment has already been sufficiently exhausted in our literature. New books of this kind should attract new subjects.

“Entertaining Arithmetic” is, for the most part, an attempt to propose a number of new, not yet developed subjects of arithmetic entertainment. Finding new topics in such a comprehensively explored area is not an easy task: the compiler cannot here use the collective work of a long series of well-known and unknown collectors, but is provided only on our own. Therefore, “Entertaining Arithmetic”, as the first attempt at updating the traditional material of such collections, should not be applied too strict a standard.

Finally, taking care that the collection was easy to read, without requiring excessive stress, the compiler avoided difficult, confusing issues and included only such material that is quite feasible for most readers. Convert have a nice game mind into a tedious task, too serious for entertainment and too fruitless for serious work - would mean perverting the purpose and meaning of this kind of literature.

Although the book is intended for readers familiar only with the elements of arithmetic, there are pages in it that may be of interest to those more knowledgeable. We earnestly ask such readers not to refuse to inform the author about the shortcomings of the book that they have noticed). For the previously given instructions, the author expresses deep gratitude to his correspondents.
Ya.P.

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CONTENT
Preface.
I. Old and new about numbers and numbering.
Mysterious signs (Task N1).
Ancient folk numbering.
Secret trading metas.
Arithmetic at breakfast (Problem N2).
Arithmetic puzzles (Problems NN3-5).
Decimal system in bookcases.
Round numbers.
II. Descendant of the ancient abacus.
Chekhov's puzzle (Problem N6).
Russian abacus.
Multiplication on abacus.
Division on accounts.
Improving accounts (Task N7).
Echoes of antiquity.
III. A little history.
"Division is a difficult matter."
Wise custom of antiquity.
Are we multiplying well?
Russian method of multiplication (Problem N8).
From the land of the pyramids.
IV. Non-decimal number systems.
Mysterious autobiography (Problems NN9–14).
The simplest number system.
Extraordinary arithmetic (Problems NN15–23).
Odd or even? (Problem N24).
Fractions without a denominator (Problems NN25–29).
V. Gallery of numerical wonders.
Arithmetic Chamber of Curiosities.
Number 12.
Number 365.
Three nines.
Scheherazade's number (Problem N30).
Number 10101 (Problem N31).
Number 10001 (Problem N32).
Six units (Problem N33).
Number pyramids (Problems NN34–36).
Nine identical numbers(Problem N37).
Digital ladder (Task N38).
Magic rings (Problem N39).
Phenomenal family (Problem N40).
VI. Tricks without deception.
The art of the Hindu king.
Without opening the envelopes (Task N41).
Guess the number of matches (Problem N42).
Reading thoughts from matches (Tasks NN43–44).
Ideal weight (Problems NN45–46).
Predict the sum of unwritten numbers (Problem N47).
Predict the result (Problems NN43–49).
Instant division.
Favorite number (Problem N50).
Guess the birthday (Task N51).
One of Magnitsky’s “comforting actions” (Problem N52).
VII. Quick counting and perpetual calendar.
Real and imaginary phenomena.
"How many weeks am I?" (Problem N53).
"How many days am I?"
"How many seconds do I have?" (Problem N54).
Techniques for accelerated multiplication.
What day of the week? (Problems NN55–57).
Calendar on the clock.
Calendar tasks.
VIII. Numerical giants.
How big is a million?
A million seconds (Problem N58).
A million times thicker than a hair (Problem N59).
Exercises with a million (Problems NN60–62).
Names of numerical giants.
Billion.
Billion and trillion.
Quadrillion.
Cubic mile and cubic kilometer.
Giants of time.
IX. Numerical Lilliputians.
From giants to dwarfs.
Lilliputians of time.
Lilliputians of space.
Super-giant and super-Lilliputian (Problem N63).
X. Arithmetic travels.
Your trip around the world.
Your ascent to Mont Blanc (Problem N64).
Plowmen-travelers (Problem N65).
An unnoticed journey to the bottom of the ocean.
Travelers standing still (Problem N66).
Out of chapters.
Curiosities: arithmetic and one more.
Objectives: mysterious autobiography; calendar tasks; The task is a joke.
Answers: to problems NN3–5; to problem N28; to problem N29; to the task of the joke.
Subject index.

Yakov Perelman, one of the most famous representatives genre of popular science literature, was born on December 4, 1882 in the county town of Bialystok, Grodno province, in the family of an accountant and a teacher. At the end primary school in 1895 he entered the Bialystok real school. While still a student at the school, in 1899 he published his first article “On the expected rain of fire” in the local newspaper “Grodno Provincial Gazette”. In August 1901, Perelman entered the Forestry Institute in St. Petersburg. Already in his first year, he began collaborating with the magazine “Nature and People”, making his debut in it with the essay “A Century of Asteroids”.

Yakov Perelman became famous in 1913, after his first book was published by Peter Soykin's publishing house. Entertaining physics". The book not only had incredible success among a wide range of readers, but was also well received in academic environment, having received more than favorable reviews from scientists.

In 1916, the second part of Perelman's Entertaining Physics was published. During his life he published a large number of popular science books devoted to various branches of science and technology, many of which have been reprinted several times and continue to be republished to this day. Visual and figurative, and most importantly, fascinating manner of presentation made his books popular among millions of readers.

In 1916, while working at the Petrograd Special Meeting on Fuel, Perelman made a proposal to move clocks forward an hour in order to save fuel, thus becoming the first in the country to propose introducing the so-called maternity leave time.

From 1918 to 1923, Perelman was an inspector of the United labor school People's Commissariat of Education of the RSFSR, taught in various educational institutions and compiled learning programs in physics, mathematics and astronomy. He was a member editorial boards magazines "Science and Technology", "Pedagogical Thought", worked in the science department of the Leningrad "Red Newspaper", and later, in the early thirties, was a member of the presidium of the Leningrad Study Group jet propulsion, where he headed the propaganda department and was involved in the development of the first Soviet anti-hail missile.

In October 1935, a unique museum he created opened in Leningrad - the House of Entertaining Science, which in a visual and cognitive form introduced schoolchildren to the achievements of science and technology. Unfortunately, almost all of the museum’s exhibits were lost during the war, and currently only descriptions of some of them have been preserved. During the siege of Leningrad Nazi troops despite hunger and difficult conditions life Yakov Perelman continued to work on articles and books, gave lectures on terrain orientation without instruments to the soldiers of Leningrad and Red Banner Baltic Fleet. Unfortunately, he did not have the chance to survive the blockade - on March 16, 1942, Yakov Isidorovich Perelman died from general exhaustion caused by hunger.

Books (35)

5 minutes to think

The book contains sections: “Problems about heaven and earth”, “Riddles of living nature”, “Deceiver feelings”, “5 minutes to think”, “Can you reason”, “Entertaining problems”, “ Interesting numbers", "Puzzles", "Funs and tricks", "Games, fun and tricks with matches", "Dominoes", "Chess", "Crosswords".

The Big Book of Entertaining Sciences

Algebra, geometry, physics, puzzles, problems, experiments.

ME AND. Perelman is a famous domestic popularizer of science, talented teacher, an outstanding wordsmith who wrote from 1913 to 1940. about a hundred popular science books addressed to the widest audience.

Among them are the famous Most of the books by Ya.I. Perelman has gone through more than 20 (!) publications, many of them translated into foreign languages and are very popular abroad.

The secret of such attractiveness of Perelman’s works lies in the fact that the author brilliantly managed to show how interesting, fascinating, even exciting the study of natural sciences: physics, algebra, geometry, usually boring, complex and uninteresting in presentation school textbooks and the majority school teachers, instilling in schoolchildren a persistent dislike of these sciences.

Quick count

The simplest and most easily learned techniques for quickly oral counting. They are designed for average abilities and do not mean public performance on stage, but the needs of everyday life.

Those who use the book should remember that successful mastery of its instructions presupposes not mechanical, but quite conscious use of techniques and, in addition, more or less lengthy training.

Perpetual motion machines. Why are they not possible?

A “perpetual motion machine” is an imaginary machine that, without borrowing energy from outside, would operate non-stop and do some work.

A machine that would continuously support only its own own movement, without performing any additional work, would not be “ perpetual motion machine"in the strict sense of these words.

Distant Worlds

"In the vast sea bright dots, dotting the starry sky, there are luminaries that are millions of times closer to us and have a completely different nature than all the other stars. At a quick glance, they are lost among thousands of others; Only sometimes the brightness of some of them and the calm, almost flickering light attracts our attention. And if, having noticed such stars, we begin to monitor them day after day, remembering their position among neighboring ones, then we will soon discover a significant feature in them...”

Live geometry textbook

Here is a book by the famous popularizer of science Yakov Isidorovich Perelman “Living Textbook of Geometry”, which is very different from the well-known “Entertaining Geometry” - mainly in its purpose: this book is more educational character. However, do not rush to put the book away.

This is by no means a dry presentation educational material. The presentation of the "Living Textbook of Geometry" is special, facilitating the assimilation of the subject. Here the inquisitive reader will find a lot of useful, interesting and accessible material, illustrated with drawings.

Entertaining arithmetic

“Entertaining Arithmetic” is, for the most part, an attempt to propose a number of new, not yet developed plots of arithmetic entertainment...

Entertaining geometry

“Entertaining Geometry” was written both for friends of mathematics and for those readers from whom for some reason many attractive aspects of mathematics were hidden...

To arouse the reader’s interest in geometry or, in the author’s words, “to instill a desire and cultivate a taste for its study is the direct task of this book”...

Entertaining geometry in the open air and at home

The book was written not so much for the friends of mathematics as for its enemies.

She does not mean mainly those who already have an inclination for mathematics, and also not those who have not yet begun to study it at all. The author intends the book primarily for that broad category of readers who became acquainted with this science at school (or are now still getting acquainted) with special interest and animation, feeding her in best case scenario only cold respect. To make geometry attractive to them, to instill a desire for it and to cultivate a taste for its study is the direct task of this book.

Entertaining mechanics

« Entertaining mechanics"- a unique manual on physics and mechanics by the outstanding popularizer of science Ya.I. Perelman, which will help develop the child’s intelligence, make it easier to assimilate the material covered in class and significantly expand school curriculum. The young reader will be offered interesting examples of the application of the basic laws of mechanics in technology, sports and even circus tricks, as well as fascinating physical quizzes.

Entertaining physics

the main objective"Entertaining physics" - to excite the activity of the scientific imagination... this is achieved by considering a motley series of puzzles, intricate questions, entertaining stories, funny problems, paradoxes and unexpected comparisons from the field of physics.

Entertaining physics. Book 2

In the proposed book, as in the first, the compiler strives not so much to impart new knowledge as to revive and refresh the simplest information on physics that the reader already has.

The purpose of the book is to stimulate the activity of the scientific imagination, to teach one to think in the spirit of physics and to develop the habit of versatile application of one’s knowledge.

Entertaining tasks and experiences

This collection includes materials from different books outstanding popularizer of science Ya.I. Perelman, the author or compiler of which he was.

The young reader will find here many interesting experiments and problems from the fields of physics, mathematics, geometry and other scientific entertainment.

Squaring a circle

From geometric problems posed by ancient mathematicians, three stand out, remarkable in that they became extremely widely known even among non-mathematicians. These tasks are briefly formulated as follows:

“Doubling the cube”: construct an edge of a cube whose volume is twice the volume of the given cube.

"Angle trisection": divide given angle into three equal parts.

“Squaring the circle”: construct a square whose area is equal to the area of the given circle.

Our brochure discusses in detail only the third, most famous of the problems listed - the proverbial squaring of the circle. The reader will learn why centuries of efforts to solve this problem have not led to success and why there is no hope of solving it sometime in the future: squaring the circle (like the other two problems on our list) is one of the unsolvable problems.

Labyrinths

The fate of labyrinths is extraordinary. From mysterious structures of ancient times, the purpose of which in many cases is a mystery to us, they gradually turned into a means of amusement and entertainment. And at the very Lately they suddenly acquire serious significance again: they are used by scientists as a convenient way to study the natural intelligence of humans and animals. The historical fates of the labyrinths are as tortuous as their own passages.

New geometry problem book

In the problem book, the compiler sought to collect possible more examples various applications of geometry in technology, natural science, world studies and everyday life, simultaneously pursuing the goal of clearly convincing of the wide and fruitful applicability of even very modest geometric knowledge.

Rocket to the moon

“As a child, it seemed to me that if you climbed onto the roof of a house, the moon would not be so far away. One moonlit evening I climbed into the attic, went to the dormer window and looked out. I thought I would see the moon up close. Where there! She still hung high in the sky, as if I was looking at her directly from the ground...”

Magic tricks and entertainment

He allows his reader to see amazing magic tricks, then revealing their mathematical secrets. The amazed reader sees extraordinary and “wonderful” things, which, as it later turns out, are based on simple arithmetic calculations.

Ya.I.Perelman collected interesting experiments and tricks that will amaze those around you, to perform which you will need the most ordinary objects that are always at hand. All this will certainly arouse your and your child’s interest in exact sciences and brighten up your leisure time.

Tsiolkovsky. Life and technical ideas

The book is dedicated to the history of life and creative technical ideas famous figure science and the brilliant inventor K. Tsiolkovsky, the creator of bold ideas for inter-sea travel, rocket engines, an all-metal airship and a number of other bold projects.

Miracle of our century

I once swore not to reveal what is described in this book to anyone. I was a 12-year-old schoolboy when I was entrusted with this secret, and I gave my word to a boy of the same age.

For a number of years, I kept the oath. Why I now consider myself free from it, you will learn from last chapter my story.

Perelman Ya.I. Big Book entertaining sciences: Algebra, geometry, physics, puzzles, problems, experiments.[Fb2- 6.7M ] [Odt- 6.7M ] [Rtf- 7.5M ] Author: Yakov Isidorovich Perelman. Compiled by D.A. Gusev.
(Moscow: AST: Astrel, 2009)
Scan, processing, Fb2 format, Odt, Rtf: ???, proofreading, editing: Raidar, 2013

SUMMARY:
Preface (3).
From the book “Entertaining Physics. Book I" (6).
From the book “Entertaining Physics. Book II" (65).
From the book “Entertaining Geometry” (123).
From the book “Entertaining Algebra” (148).
From the book “Entertaining Arithmetic. Mysteries and wonders in the world of numbers" (165).
From the book “Living Mathematics. Mathematical stories and puzzles" (192).
From the book “Entertaining tasks and experiments” (218).

Publisher's abstract: ME AND. Perelman (1882-1942) - a famous Russian popularizer of science, a talented teacher, an outstanding master of words, who wrote from 1913 to 1940. about a hundred popular science books addressed to the widest audience. Among them are: famous works, such as “Entertaining Physics”, “Entertaining Arithmetic”, “Living Mathematics”, “Entertaining Geometry”, “Entertaining Algebra” and many others. Despite the fact that the first of them appeared at the beginning of the 20th century, they are still relevant and interesting to this day. Most of the books by Ya.I. Perelman's work has gone through more than 20 (!) editions, many of them have been translated into foreign languages and are very popular abroad. The total circulation of his works in our country exceeds 15 million copies, and yet many of his books were bibliographic rarities in their time; readers stood in line for them in libraries.
The secret of such attractiveness of Perelman’s works is that the author brilliantly managed to show how interesting, fascinating, even exciting the study of natural sciences can be: physics, algebra, geometry, which, as a rule, are boring, complex and uninteresting in the presentation of school textbooks and most school teachers , instilling in schoolchildren a persistent dislike of these sciences.
ME AND. Perelman is the only author in our country (and perhaps in the world) who has created such successful works of the popular science genre. Today's schoolchildren and students, as a rule, know little about them and are sometimes deprived of the joy of communicating with Perelman's entertaining science.
The proposed anthology is a collection of the most striking and important (from the point of view of the compiler) passages from various books by Ya.I. Perelman. The reader can be recommended to schoolchildren and students as an auxiliary and additional material for courses in physics, algebra, geometry (for school), mathematics, logic, concepts modern natural science and philosophy (for universities). This reader is intended to show schoolchildren and students that studying various sciences can be not only difficult and tiring, but also pleasant and exciting no less than the activities to which they devote their hours of rest and leisure...

PREFACE

There are a number of original and translated collections in Russian*), generally pursuing the same goal as this book: to revive school mathematics by introducing interesting problems, entertaining exercises, and interesting theoretical and practical information. Those familiar with this literature are well aware that most of these books assiduously draw their material from the same limited fund accumulated over centuries; hence the close similarity of these works, which develop, with varying detail, almost the same themes. But the traditional inventory of mathematical entertainment has already been sufficiently exhausted in our literature. New books of this kind should attract new subjects.

*) Among them famous collection E. I. Ignatiev “In the kingdom of ingenuity* (of his three books, the 2nd and 3rd were compiled with the participation of the author of the proposed collection) almost exhausts all the “classical* material of arithmetic entertainment.

“Entertaining Arithmetic” is, for the most part, an attempt to propose a number of new, not yet developed plots of arithmetic entertainment. Finding new topics in such a comprehensively explored area is not an easy task: the compiler here cannot use the collective work of a long series of well-known and unknown collectors, but is left only to his own strength. Therefore, “Entertaining Arithmetic”, as the first attempt at updating the traditional material of such collections, should not be applied too strict a standard.
Another feature of the proposed collection is that it is limited to purely arithmetic material, trying to be as close as possible to the various departments of school arithmetic. Entertainment, although entertaining, but not affecting any of its departments, did not find a place in the book.
Finally, taking care that the collection was easy to read, without requiring excessive stress, the compiler avoided difficult, confusing issues and included only such material that is quite feasible for most readers. To transform a pleasant game of the mind into a tedious activity, too serious for entertainment and too fruitless for serious work, would be to pervert the purpose and meaning of this kind of literature.
Although the book is intended for readers familiar only with the elements of arithmetic, there are pages in it that may be of interest to those more knowledgeable. We earnestly ask such readers not to refuse to inform the author about the shortcomings of the book that they have noticed *). For the previously given instructions, the author expresses deep gratitude to his correspondents.
Ya.P.
*) Address for correspondence: Leningrad, Stremyannaya street. 4. Cooperative Publishing House "Time". Yakov Isidorovich Perelman.

Chapter I

OLD AND NEW ABOUT NUMBERS AND NUMERATION
MYSTERIOUS SIGNS

“Similar signs have been seen in many houses on the back stairs at the doors of apartments. Typically, signs of this type are available at all doors of a given house, and no two identical signs are observed within the same house. Their gloomy outline naturally instills anxiety in the residents. Meanwhile, their meaning, quite innocent, is easily revealed if you compare them with the numbers of the corresponding apartments. So, for example, I found the above signs at the doors of apartments No. 12, No. 25 and No. 33:

“It is not difficult to guess that the crosses mean tens, and the sticks mean units; This turned out to be the case in all cases that I observed without exception. This peculiar numbering obviously belongs to Chinese janitors* who do not understand our numbers. These signs appeared, one must think, even before the revolution, but only now they attracted the attention of alarmed citizens.”
*) There were many of them in Leningrad then. Later I found out that Chinese character for yu it has exactly the indicated cross shape (the Chinese do not use our “Arabic” numerals).
Mysterious signs of the same outline, but not with straight, but with oblique crosses, were also discovered in houses where Russian peasants who came from the villages served as janitors. Here it was no longer difficult to find out the true authors of the secret writing, who had no idea that their artless designations of apartment numbers were only now noticed and caused such a commotion.

OLD FOLK NUMBERING
Where did Leningrad street cleaners get this simple way of designating numbers: crosses for tens, sticks for units? Of course, these signs were not invented in the city, but were brought from their native villages. This numbering has long been in wide use and is understandable to everyone, even the illiterate peasant in the most remote corner of our Union. It goes back, without a doubt, to ancient times and is used not only among us. Not to mention the relationship with Chinese notations, the similarity of this simplified numbering with the Roman one is also striking: in Roman numerals, sticks mean units, oblique crosses mean tens.
It is curious that this popular numbering was once even legalized in our country: according to exactly this system, only more developed, tax collectors were supposed to make entries in the tax notebook. “The collector,” we read in the old Code of Laws, “accepting money from any of the householders brought in to him, must himself, or through a clerk, write down in the tax notebook against the name of the householder whose date how much money was received, indicating the amount of the amount accepted numbers and signs. For the information of everyone, introduce these signs everywhere that are the same, namely:
ten rubles means a square sign;
ruble circle;
ten kopecks X oblique cross;
penny I stick;
a quarter is a dash.
For example, twenty-eight rubles fifty-seven kopecks three quarters:
Elsewhere in the same volume of the Code of Laws we find once again mention of the mandatory use
folk numerical designations. Special signs are given for thousands of rubles - in the form of a six-pointed star with a cross in it, and for one hundred rubles - in the form of a wheel with 8 spokes. But the designations for the ruble and ten kopecks are established here differently than in the previous law.
Here is the text of the law about these so-called. "yasak signs":
“So that on every receipt issued to the Noble Headman, from whom yasak will be paid, in addition to the presentation in words, it should be shown special signs the number of rubles and kopecks deposited so that those submitting a simple count of this number can be confident in the validity of the reading ‘). The signs used in the receipt mean:
(star) - one thousand rubles,
(wheel) - one hundred rubles,
square - ten rubles,
X cross - one ruble,
IIIIIIIIII - ten kopecks,
I - 1 kopeck.
“So that no additions can be made here, all such signs should be outlined in a circle with straight lines. For example:
1232 rub. 24 k. is depicted like this: (see figure).
As you can see, the Arabic and Roman numerals we use are not the only way number designations. This shows that the signs described were in widespread use among the population.
In the old days they were used here, and even now other systems are used in villages written notation, vaguely similar to Roman numerals and not at all similar to Arabic numerals.
But this is not all the ways of depicting numbers that are used today: many merchants, for example, have their own secret signs for numerical designations, the so-called. trading "metas". Let's talk about them in more detail now.

SECRET TRADING METS

On things purchased from retailers or private stores, especially provincial ones, you have probably noticed sometimes incomprehensible letter designations like
and her in oo.
This is nothing more than the price of a thing without asking, which the merchant marks on the product for memory, but in such a way that the buyer cannot guess it. Having glanced at these letters, the merchant immediately penetrates into them hidden meaning and, having made an extra charge, tells the buyer the price with the request.
This designation system is very simple, if you only know the “key” to it. The merchant chose a word made up of 10 different letters; most often they chose words: hard work, justice, Yaroslavl, peace-lover, Miralyubov. The first letter of the word means - 1, the second - 2, the third - 3, etc.; The tenth letter denotes zero. With the help of these conventional letters and numbers, the merchant indicates their price on the goods, storing them in strictly confidential"key" to its notation system.
If, for example, the word is selected:
justice
1234567890
then the price is 4 rubles. 75 k. will be designated as follows:
in uo
The sign “poe” means 1 rub. 50 k. (150), pse - 1 ruble (100), etc.
Sometimes the price on a product is written as a fraction; for example, on one of the books I bought there is the designation
oe/tro.
This means, with the key “hard work”, that you need to request 1 rub. 25 kopecks, but the book itself cost 50 kopecks.
Traders strictly guard the secret of their meta. But if you buy several things in the same store, then, by comparing the price named by the merchant with the corresponding symbols, it is not difficult to guess the meaning of the letters. It is especially easy to solve the meta tags of cheap goods, where they ask for little, so that the first digits of the amounts paid answer initial letters designations. Having solved a few letters, it is easy to find out the meaning of the rest. With some insight, the “key” of any meta can be unraveled.
Let's say, for example, that you bought several things and paid 25 for the first, 22 for the second, and 28 kopecks for the third. In the corners of these objects you find such symbols
ro, rr, rd.
It is clear that the letter p means 2. Having guessed, using other goods, another letter, for example, c - 6, you will already guess that the key is justice. Number suitable words, it should be noted, is limited, and the choice is not overly difficult.

ARITHMETIC AT BREAKFAST

After what has been said, it is easy to realize that numbers can be represented not only with the help of numbers, but also with the help of any other signs or even objects - pencils, pens, rulers, rubber bands, etc.; you just need to agree to attribute to each object the value of some specific number. You can even, for the sake of curiosity, use such figures-objects to depict operations on numbers - add, subtract, multiply, divide. Here, for example, is a series of actions on numbers, indicated by table setting items (see figure). Fork, spoon, knife, jug, teapot, plate - all these are signs, each of which replaces a certain number.

Task No. 2.
Looking at this group of knives, forks, dishes, etc., try to guess: what exactly are the numbers indicated here? At first glance, such a task seems very difficult: you have to solve real hieroglyphs, as the Frenchman Champollion once did. But your task is much easier: you know that the numbers here, although indicated by forks, knives, spoons, etc., are written according to decimal system notation, i.e. you know that the plate in second place (counting from the right) is the tens digit, that the object to the right of it is the units digit, and left side- hundreds figure.
In addition, you know that the arrangement of all these objects has a certain meaning, which follows from the essence arithmetic operations, produced on the numbers they indicate. All this can significantly contribute to the proposed task
make your decision easier.

END OF BOOK FRAGMENT

Name: Interesting arithmetic. 1926.

There are a number of original and translated collections in Russian that generally pursue the same goal as this book: to revive school mathematics by introducing interesting problems, entertaining exercises, and interesting theoretical and practical information. Those familiar with this literature are well aware that most of these books assiduously draw their material from the same limited fund accumulated over centuries; hence the close similarity of these works, which develop, with varying detail, almost the same themes. But the traditional inventory of mathematical entertainment has already been sufficiently exhausted in our literature. New books of this kind should attract new subjects.

Another feature of the proposed collection is that it is limited to purely arithmetic material, trying to be as close as possible to the various departments of school arithmetic. Entertainment, although entertaining, but not affecting any of its departments, did not find a place in the book.
Finally, taking care that the collection was easy to read, without requiring excessive stress, the compiler avoided difficult, confusing issues and included only such material that is quite feasible for most readers. To transform a pleasant game of the mind into a tedious activity, too serious for entertainment and too fruitless for serious work, would be to pervert the purpose and meaning of this kind of literature.
Although the book is intended for readers familiar only with the elements of arithmetic, there are pages in it that may be of interest to those more knowledgeable. We earnestly ask such readers not to refuse to inform the author about the shortcomings of the book that they have noticed). For the previously given instructions, the author expresses deep gratitude to his correspondents.
Perelman Ya.I.

CONTENT
Preface.
I. Old and new about numbers and numbering.
Mysterious signs (Task N1).
Ancient folk numbering.
Secret trading metas.
Arithmetic at breakfast (Problem N2).
Arithmetic puzzles (Problems NN3-5).
Decimal system in bookcases.
Round numbers.
II. Descendant of the ancient abacus.
Chekhov's puzzle (Problem N6).
Russian abacus.
Multiplication on abacus.
Division on accounts.
Improving accounts (Task N7).
Echoes of antiquity.
III. A little history.
"Division is a difficult matter."
Wise custom of antiquity.
Are we multiplying well?
Russian method of multiplication (Problem N8).
From the land of the pyramids.
IV. Non-decimal number systems.
Mysterious autobiography (Problems NN9-14).
The simplest number system.
Extraordinary arithmetic (Problems NN15-23).
Odd or even? (Problem N24).
Fractions without a denominator (Problems NN25-29).
V. Gallery of numerical curiosities.
Arithmetic Chamber of Curiosities.
Number 12.
Number 365.
Three nines.
Scheherazade's number (Problem N30).
Number 10101 (Problem N31).
Number 10001 (Problem N32).
Six units (Problem N33).
Number pyramids (Problems NN34–36).
Nine identical numbers (Problem N37).
Digital ladder (Task N38).
Magic rings (Problem N39).
Phenomenal family (Problem N40).
VI. Tricks without cheating.
The art of the Hindu king.
Without opening the envelopes (Task N41).
Guess the number of matches (Problem N42).
Reading thoughts from matches (Tasks NN43–44).
Ideal weight (Problems NN45–46).
Predict the sum of unwritten numbers (Problem N47).
Predict the result (Problems NN43–49).
Instant division.
Favorite number (Problem N50).
Guess the birthday (Task N51).
One of Magnitsky’s “comforting actions” (Problem N52).
VII. Quick counting and perpetual calendar.
Real and imaginary phenomena.
"How many weeks am I?" (Problem N53).
"How many days am I?"
"How many seconds do I have?" (Problem N54).
Techniques for accelerated multiplication.
What day of the week? (Problems NN55–57).
Calendar on the clock.
Calendar tasks.
VIII. Numerical giants.
How big is a million?
A million seconds (Problem N58).
A million times thicker than a hair (Problem N59).
Exercises with a million (Problems NN60–62).
Names of numerical giants.
Billion.
Billion and trillion.
Quadrillion.
Cubic mile and cubic kilometer.
Giants of time.
IX. Numerical Lilliputians.
From giants to dwarfs.
Lilliputians of time.
Lilliputians of space.
Super-giant and super-Lilliputian (Problem N63).
X. Arithmetic Travels.
Your trip around the world.
Your ascent to Mont Blanc (Problem N64).
Plowmen-travelers (Problem N65).
An unnoticed journey to the bottom of the ocean.
Travelers standing still (Problem N66).
Out of chapters.
Curiosities: arithmetic and one more.
Objectives: mysterious autobiography; calendar tasks; The task is a joke.
Answers: to problems NN3–5; to problem N28; to problem N29; to the task of the joke.
Subject index.

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