All-Soviet Union math competition

"This file contains the problems, suggested for solving on the Russian national mathematical competitions
(final part).
I've posted this stuff in a number of articles in rec.puzzles. But I have got many requests for the missing
parts. So I have decided to put this material here, having provided it with the answers on the common
questions.
==================collected articles start======================
I'm going to send some problems from the book Vasil'ev N.B, Egorov A.A. "The problems of the All-
Soviet–Union mathematical competitions",–Moscow.:Nauka. 1988 ISBN 5–02–013730–8. (in Russian).
Those problems were submitted for the solving on the competition between the pupils of 8, 9, or 10 forms
for 4 hours. So they do not contain something of the advanced topics, –– all of them can be solved by a
schoolboy. They can not go out of the common school plan bounds.
Most of the problems are original and the book contains all the necessary references. I am not going to
translate all the book, so I shall not send the solutions. Please, accept those messages as they are, to say
more exactly – as I can. I have to do my job, and this is hobby only, but nevertheless, that should be
enjoyable to solve those problems.
"Nobody can embrace the unembraceable."
Kozma Prutkov.
(beginning of the XIX c.)
May be those postings are just a harassment, but I hope, that most of You will not only enjoy the problems
solving, but will be able to use them in Your work with the students.
"Zeal overcomes everything."
"Sometimes zeal overcomes even the common sense."
Kozma Prutkov.
There are some wonderful books in Russian, that have not been translated into English yet, for example,
"Problems of the Moscow mathematical competitions",–compiled by G.A.Galperin, A.K.Tolpygo.,–
Moscow, Prosveshchenie, 1986.
A.A.Leman "Collection of Moscow mathematical competitions problems", –Moscow, Prosveshchenie,
1965."


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