Mathematical Olympiad at MESI

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I’m not at all familiar with such words as “non-relativistic” quantum mechanics, etc. I would like the material to be presented in a simpler form and really be aimed at non-specialized school students in grades 9-10.”
We are very grateful to Gala for this letter. After all, letters also help us in our work.
The editors believe that Gali’s claims are fair. When posting articles of increased difficulty, we will stipulate this each time and, of course, explain the meaning of incomprehensible expressions.
We would like more readers to weigh in on this matter.
Sometimes «Kvant» turns out to be a family magazine. Here is what Natasha Sukuasova from Kharkov writes: “I love mathematics, my brother is interested in physics; We are collecting a library in which your magazine occupies an important place. We store all numbers «Kvant»; it is often necessary to list individual articles several times.”
It is also pleasing that non-traditional readers thank the editors for “the concrete, highly effective assistance” (S. Berementein, Moscow).
Thus, V. Balabanov from Novokuznets reported that work on materials placed in «Kvant» under the heading “Applicant Practice” helped him to enter the institute. G. Zaitsev (Gagra) spoke even more specifically: “During the days of passing the entrance exams to the university, I met comrades who were of the same opinion with me about the great usefulness of the magazine «Kvant», especially its sections under the headings “Problem” «Kvant» and “Applicant Practice.” The experience of entrance exams finally convinced us of this.”
A number of letters contain the wishes of the editors. Thus, a senior employee from Bryansk, V. Chutov, expressed the opinion: “I would like there to be more materials about the newest, so to speak, the most recent achievements of mathematics, review articles at a popular level on various modern branches of mathematics.”
Some readers emphasize their desire to see a more complete “Laboratory” section «Kvant», others ask for an expanded section of puzzles, paradoxes, games and tricks…
These wishes of our readers are fully justified, and we will try to satisfy them next year.
The editors are grateful to the readers who sent specific critical comments on the materials, which are placed in «Kvant».
We are deeply grateful to all the readers who have written to us, with a heterpene jam of letters in the coming year.
V. N. Berezin, M. L. Smolyansky

Mathematical Olympiad at MESI

In 1932, the Moscow Economic and Statistical Institute was created. Now it occupies a leading position in the country in training specialists related to machine data processing necessary for managing complex systems.
This academic year will see the first graduation from the Faculty of Economic Cybernetics. The faculty trains mathematical engineers in computer software, as well as specialists in the use of mathematical methods in economics.
The use of modern computers is unthinkable without mathematics. That is why, when entering college, applicants will take two exams in mathematics. For the first time this year, exams in physics were taken using a computer.
This year, MESI is holding the 2nd Mathematical Olympiad for graduating high school students. The Olympiad is held in two types: I - correspondence, II - full-time.
Kuchasia in the second round is accepted by schoolchildren who have successfully completed the task of the first round and sent solutions no later than January 15, 1972 (by postmark). The full-time round will be conducted taking into account the computer (see «Kvant» No. 10, 1971). Each Olympiad participant admitted to the second round will be notified at the address indicated by him. Success in the Olympiad will be taken into account when entering the institute.
Solving problems must be completed in Russian in a student’s notebook. Our address: Moscow, G-435, V. Savinsky lane, 14, “Olympiad”.

First round problems

1. Prove that if the sides of a right triangle are arithmetic-progressive, then its difference is equal to the radius of the inscribed circle.
2. Solve equation x! +y! = (x + y)! (if n! = 1·2·3·4…n).
3. Prove that if two equations take into account the computer (see «Kvant» No. 10, 1971). Each Olympiad participant admitted to the second round will be notified at the address indicated by him. Success in the Olympiad will be taken into account when entering the institute.
4. How many terms of the sum 1+2+3+… do you need to take to get a three-digit number consisting of identical digits?
5. Balls of the same radius are laid once in the shape of a square, and another time in the shape of a regular triangle. Find the number of balls if it is known that there are two fewer balls along the side of the square than along the side of the triangle.
   N. G. Venetsky, Yu. I. Sorkin