# e-book 60 Odd Years of Moscow Mathematical Olympiads Contents:

Moskowitz Solutions by Martin Erickson Hardy, Edward M. Wright Zuckerman Samuel Greitzer Lausch, Peter J.

Taylor Cohen Bradley Yaglom, I. Yaglom Posamentier, Charles T. Salkind Vilenkin Hirst Olds Martin Sierpinski Prasolov Young Stanley Ogilvy Stanley Ogilvy, John T. Anderson Maxwell Petkovic scanned. Petkovic Vorobyev Small Kazarinoff Yaglom, Allen Shields split pages.

Yaglom, Allen Shields Coxeter, S. Greitzer Murty Hall, S. Knight Polya PDF split p.

### latest added, problem collections, in this blog

Polya - DJVU p. Polya DJVU p. Polya PDF p. Sova Hajos, G. Neukomm, J. Suranyi, Andy Liu split pages. Suranyi, Andy Liu Taylor, AM Storozhev Branzel, I. Serdean, V.

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## The problems of the All-Soviet-Union mathematical competitions 1961-1986

Serdean D 86 p. Li p. Li 79 p. Merrill I by Ross Honsberger II by Ross Honsberger III by Ross Honsberger Casti Goucher Andreescu, Z. Feng p. Schoenfeld Kendall, G. Thomas Mira I - Induction and Analogy in Mathematics by G. Polya Santos 98 p.

Santos p. Mildorf 34 p. Kuczma split. Erickson, Joe Flowers Pranesachar Greenes Larson split pages.

## Library Holdings – Mathematics – Al-Hikmah University, Ilorin

Problem 8. Prove that it is impossible to divide a scalene triangle into two equal triangles. Two circles are tangent externally at one point. Common external tangents are drawn tothem and the tangent points are connected. Prove that the sum of the lengths of the opposite sides of thequadrilateral obtained are equal. See Problem 8. Find three-digit numbers sucvh that any its positive integer power ends with the same threedigits and in the same order.

For which a the number of solutions of the system is equal to three or two? Prove that point A fills in a line segment and findits length. Tour 8. Given the 6 digits: 0, 1, 2, 3, 4, 5.

Find the sum of all even four-digit numbers which can beexpressed with the help of these figures the same figure can be repeated. Suppose we have two identical cardboard polygons. We placed one polygon upon the otherone and aligned. Then we pierced polygons with a pin at a point. It turned out that the polygons coincided aligned again. What is the minimalpossible number of sides of the polygons? The nearest to Adivision point P is connected with B. A circle rolls along a side of an equilateral triangle.

The radius of the circle is equal to theheight of the triangle. Olympiad 9 Tour 9. What is the largest number of acute angles that a convex polygon can have? Find a four-digit number such that the remainders after its division by and are and 98, respectively. Prove that after completing the multiplication and collecting the termshas no monomials of odd degree.

Through a point M inside an angle a line is drawn. It cuts of f this angle a triangle of theleast possible area. Prove that M is the midpoint of the segment on this line that the angle intercepts. Prove that for any positive integer n the following identity holds 2n! How many eightthgraders took part in the tournament? Find x for which the length of MN is minimal. The distances between the consecutive towns areequal. Each of the towns is the point of origin of a straight highway.

The highways are on the same side of MN and form the following angles with it:No. Eachintersection has a gate. As soon as the first in time, not in number car passes the intersection the gate closesand blocks the way for all other cars approaching this intersection.

## 60-odd YEARS of MOSCOW MATHEMATICAL OLYMPIADS

Which cars will pass all intersectionsand which will be stopped? A bus network is organized so that:1 one can reach any stop from any other stop without changing buses;2 every pair of routes has a single stop at which one can change buses;3 each route has exactly three stops? How many bus routes are there? Ninth and tenth graders participated in a chess tournament. There were ten times as manytenth graders as ninth graders. The total score of tenth graders was 4. What was the ninth graders score? Given the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8,.