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Old textbooks of the USSR

Purpose: The book of Hungarian mathematicians is devoted to mathematical logic

Publisher: "Mir" Moscow 1975

Format: DJVU, File size: 9.07 MB.

The preface of the translator 5.

Preface 7.

Several party words to reader 9

Instead of the substantial pointer 16

TASKS

Part I. First Acquaintance 17

Part II. Two measurements 21.

Part III. Three dimensions 33.

Part IV. Not everyone should cut under one comb 36

Part V. without template 39

See Table of Contents ...

SOLUTIONS

Part II 123.

Conclusion. What we learned

about two-dimensional logical tasks? 168.

Part III. 177.

Instead of imprisonment 265.

Part IV 266.

Not everything should be cut under one comb 344

Part V. 343.

Download USSR textbook - Game and logic 85 logical tasks of 1975

Open - Excerpt from the textbook

The book of Hungarian mathematicians D. Bizama and Ya. Herzeg is dedicated to mathematical logic.

The book is equipped with a carefully developed system of special pointers that help to navigate the features of the tasks.

The book is of interest to the widest circles of readers - entertaining mathematics lovers.

The editorial office of scientific and popular and science fiction literature.

Preface translator

Logical tasks are loved by our reader's audience. Some see their kind of "gymnastics of the mind" in them, a means of quenching natural for every thoughtful man needs to experience and exercise their own impact. Others attracts an elegant literary shell: Fabul logical tasks is often very entertaining. Third consider their accessibility to be the main advantage of this species: it is often possible to hear that there are not special knowledge to solve logical tasks, but only a certain level of development, the ability to logically think, acquired and developed, as any other skill, persistent exercises.

Nowadays, the Russian translation of the book of Hungarian mathematicians D. Bizama and J. Herzega "Game and Logic is offered to the court. 85 logical tasks.

Initially, the authors wanted to call their book "School of Thinking". And indeed, opening the book, the reader enters the exemplary school, where two teachers, tactful and benevolent, teach everyone who wants, the art of solving logical tasks. (I am afraid that the mention of the school can create some potential readers for the idea of \u200b\u200bthe book and to beat off the hunt to get acquainted with it in more detail. Do not hurry! In this school really teach logic, but do it playing. In her walls there is no place to be sad and bored!)

The traditional means of solving the logical tasks - table, in the cells of which all sorts of combinations of the elements of the sets under consideration are inscribed - in the hands of the Bizam and Hercega turns into a tool of extraordinary power and flexibility. The table allows you to solve logical tasks, and not just decide, but also to find the optimal (minimal by the number of "elementary" conditions) solutions. The table helps to analyze the conditions of the problem, detect redundancy, check the consistency and completeness, as well as the possibility of splitting the initial task to independent "subtasks". The table allows you to set the equivalence externally, it would seem different tasks and, lifting a logical skeleton in verbal clothes, design new logical tasks with predetermined properties.

Lathe in medieval universities, the "table language" is mandatory for all who crosses the threshold of the School of Bizam and Hercega. Not trouble, if you did not own them before! You are provided with a unique opportunity to do it now. The course of direct and reverse translation is so intense, and "spoken practice" is so extensive that you will very soon learn to speak in tabular language without the slightest accent and independence about yourself to achieve the highest degree of language proficiency - the ability to think on it. It is necessary to say whether an important role is played by the special "tabular" thinking today, when the methods of the so-called final mathematics not only gained citizenship rights in the most mathematical science, but also are widely used abroad.

But there would be no high goal in front of themselves the authors, it would be impossible to achieve them if they could not find an unusually bright form to embody their ideas - the game itself, which throughout the book goes hand in hand with logic. There is no need to list all the techniques and tools that use the Bizam and Herceg: Dry List (and even detailed retelling) is powerless to convey the originality of their books - it needs to be read, reading not in a hurry, with a pencil in his hand, following all the advice of authors.

So welcome to school thinking!

Some of these tasks have already been published in the Hungarian Scientific and Popular Weekly "Life and Science" in the section "School of Thinking" (even before this section began to appear the tasks of Logar Mishki1) 2. It was during the work that in this section of the journal we had the idea that the materials published in it, properly ordered and supplemented, could be published with a separate book.

The selection and systematization of logical tasks undoubtedly should be started from splitting them to types. The material of the book, as if melting during the work, forced us to constantly make certain improvements until finally crystallized the sequence of linked types of logical tasks, the detailed presentation of which was the main topic of our entire book.

Carefully systematizing the assembled material, we set out it in the form of tasks, problems. Of the 85 tasks included in the final version of the manuscript, only 8 were borrowed from other sources (tasks 1, 2, 3, 4, 79, 80, 81 and 82), but even these tasks were partially reworked, and solutions in all without Excluding cases are written again. All other tasks are original. We would like to hope so that the content of the entire book can be considered more or less new. However, it is quite possible that we never managed to achieve the goals set in front of ourselves, and we will accept all the critical comments with gratitude.

Taking this opportunity, we would like to thank everyone who suggested us about creating a book: the editors of the magazine "Life and Science", the editor-in-chief of the journal "Fenia Bela", the staff of the department "School of thinking" (without valuable tips Which this book would hardly have been written), readers of the magazine that corrected the mistakes seen by them and express many critical comments and instructions. Finally (but not least), we thank the publishing staff and everyone who took part in the work on the book.

Differ Bizam Janos Herceg

1 Character, the name and surname of which in Hungarian reminds the word "logarithm". - approx. Translate

2 We've even been going to call our book "School of Thinking" - this is the name of how it is impossible to suit her content however, we had to abandon our intention, because the Hungarian translation of the book of famous mathematics and teacher of Professor Professor Book of famous Mathematics was published Understand how to solve the task, state. Educational and pedagogical publishes of the Ministry of Education of the RSFSR, M., 1959).

Several partic words to the reader

30-40 years ago, mathematics, by general, was the true "scarecrow". It is clear that with such a respect to mathematics for a small exception, no one knew, and I could not know. And although now they treat mathematics completely differently, sometimes you still have to hear the echoes of the past, and unfortunately, it is not so rare. Many believe (especially if their acquaintance with mathematics was limited to those knowledge they made from high School) that they have no mathematical abilities. Meanwhile, the like opinion is often erroneous.

The school program in mathematics sets a two-way task: first, to promote the development of logical thinking and, secondly, to give them specific mathematical knowledge. Not all children make this dual load. And yet the second task cannot be separated from the first. If anyone has not learned educational material, Whatever mathematical abilities he possessed, he will not be able to keep track of the progress of reasoning. Without understanding the explanation of the teacher, such a person begins to experience the "absence" of his mathematical abilities and ceases to do mathematics at all.

While working on a book, we watched a special attention to not miss the interests of this circle of readers. It seems to us that we have achieved the goal: for understanding the book no preliminary knowledge is required. It is only necessary to learn what is written in our book. If anyone takes the work to break all the tasks from the first to the last (and at the same time will taste their decisions with those in our book), then you can challenge that the content of the book will be "native elements" for him and everything will be clear.

For our part, we want to help the reader in mastering mathematical thinking and prompt him the direction in which its abilities should be developed. For example, tasks in the book are not as necessary, but in such a sequence that should help the reader guess the solution. For the same purpose, the sections in which are perfect in terms of the unity of the book, in which we are talking On the conformity between the tasks and decisions belonging to different directions. Sometimes (this happens quite rarely) we still have to refer to certain mathematical facts. However, these sections reader without prejudice to understanding further can miss.

In the same spirit, the tasks in the section "School of Thinking" of the Hungarian Scientific and Popular Weekly "Life and Science" were supposed. Work in the editorial office of this section served for us a good school. During the four-year term of existence, the number of letters sent to the editor with tasks decisions increased by about 10 times. From these letters, we not only learned what tasks are particularly loved by readers, but also met with the most common mistakes and typical deformity solutions.

We believe that it makes sense from one topic to another in mathematics only when you thoroughly figured out in the previous topic, feel it, "like at home." The versatility of knowledge is acquired with experience, in the process of solving the tasks arising in the course of studying the topic. In our book, the tasks are grouped by topics. However, they may seem the same only with the most superficial acquaintance. Attentive reader will immediately see that there are no two tasks in the whole book that coincide to the smallest details. Each task certainly contains some new, additional barcode that distinguishes it from the previous one.

Popular mathematics is not alien to the concern for the external form of the presentation. Mondering for this, we sought to express the tasks in the "non-serious", "toy" form. However, their entertaining form lies quite serious content. As for decisions, they will only interest those readers who love to break their heads over a difficult task.

Of course, we are well aware of how many of our readers are varied, how many of their requirements are. Since we wanted to satisfy requests as much as possible a wide range of readers, we tried to envisage that everyone could extract something useful for himself from it.

Our task was facilitated by the fact that some readers sent us their proposals, they reported, in what sequence, in their opinion, there would be tasks to be located.

Each of the types of readers (with the exception of type a) we have appropriated a special mark. He seems to serve as a signal for which the reader can easily recognize the tasks that, in our opinion, he should decide.

Seeing the picture of this game it seemed to me that I had already seen something in my distant childhood.
After reading the description of the product accurately understood that game - modern The version of the very old Soviet game "Logic". It is a pity that I will not find rarity (35 years has already passed), but I will try to compare the Soviet and Chinese versions of this game by memory.

Delivery occupied exactly a month. In the mail received a huge package weighing just over 500 grams. Was amazed. In the picture, the dimensions of the game are not clear, I did not read in the description, as I remember that the Soviet toy was about 200 mm x 70 mm.

Inside the package box with the game. Packed disgusting. Mail from the box did not leave the box, but the contents did not suffer. Because Planned when ordering a toy for myself, I did not upset about the package.

Equipment:

Gaming field;
Stand;
Encoder;
Package with color "codes";
Instructions in English.

The game is completely made of plastic. There is no smell. Game field 350 mm long width 95 mm. On the field there are depresses for the "code" pins 12 rows of 4 pieces in each. At the bottom of the field container for pins. Closed with a transparent lid. The cover is a loose, when you turn the toy all the contents on the floor. On the boxes of the field of 12 extended plates of white and red. Each numbers are numbered 1-2-3-4.

On the underside of the field there is a transverse wheelter for the possibility of rolling the playing field between players relative to the central platform. Really convenient.

This is how the prepared game looks like.

The code is exhibited in such a cylinder. On it, comfortable legs, does not ride on the table. The "code" in the windows sits deeply, so it is visible only to the "encrypter".

From above, the cylinder is "gear" code change.

Skins of a set of just 96 pieces of 8 colors

The instruction is not colored, sorry. I do not understand why it is difficult to make high-quality printing.

How to play I remember very vaguely. That was a long time ago. But I found a description of the game Hasbro "The Lord of the Mind", I think the Chinese and were inspired by the product of this manufacturer and copied it.

Purpose of the game: bypass the opponent, inventing his cunning code or hacking its code
In the role of an encrypter: Your goal is to make such a cunning code so that your opponent will solve it as long as possible.
In the role of a decrypter: you have to solve secret code For the smallest number of attempts.

Preparing for the game: Pull the pins into the pallet for pins and throw away the package. Make sure the red and white indicator levers are filled in. Before starting the game, agree on the number of games that you will play, it must be even.

The order of the game: Determine who will be the first encrypter. This player raises the secret screen at the end of the block and inserts four code pin (its secret code) into the opening from the bottom. Note: Make sure the block is located so that the decryllor cannot see the code! You can not use two or more pins of one color. After installing the code, the decryllor can begin to guess it, trying to repeat the exact color and position of the hidden code pins. Each attempt consists in placing a number of code pins on the block. Each series of pins should remain in place during the game. After each attempt to solve the code encrypter must inform the decrypter about its progress in guessing the code, using the indicator levers (on both sides of the block) as follows:

Red Indicator levers: pull the appropriate red lever to show the number of pins of the right colors in the correct position.

White indicator levers: pull the appropriate white lever to show the number of pins of the right colors, but in the wrong position

If the decryllor is guessing the secret code, the encryptionman pulls the red indicator lever closest to the correct combination, so that it shown the number 4 and discloses the secret code, turning the unit back side. The game ends. Count the glasses and change the roles.

Account management ... At the end of each game, the encrypter receives one point for each row of code pins sent by the decrypter. If the decryllor does not guess the code for 9 attempts, the game stops and the encrypter receives 9 points. Record your glasses after each game. At the end of each game, players change roles. Upon completion of the number of games you agreed, summarize your glasses - the winner becomes the player with the greatest points.

Errors: If when informing an decryptor, encrypter makes a mistake, the game is replaying and the decryllor receives 3 extra points.

Played with my daughter. I realized that with logic in girls "not very" :).
With my prompts, she was still able to win. She liked the game.

Now the promised comparison with the Soviet "logic".

The game field is simply a huge and sleeve large, children are conveniently visually and tactile.
IN soviet game All the miniature and pry the sleeper code for me was problematic.

Encifrator is a separate element and is protected from peeping.
In the domestic cipher, recruited from one end of the field, which did not allow the possibility of moving the field to the player who guess the code.

In an overlooking game, tips (plates with sides) are very simply implemented.

Cons (in no way affect the gameplay):

Container cover without latch. We will collect any seal. Otherwise, during transport, all the sleeves are lost.

Inside the color encoder pale. Although, it can specifically not spy.

Printing instructions and packaging.

Everything. Thank you all and successful purchases!

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