MMT
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ball or not (but it is impossible to know how many such balls are in the pile). Prove that in 8 tests it is possible to isolate both radioactive balls.
- Of the 11 balls, 2 are radioactive. Prove that in less than 7 checks it is impossible to guarantee the release of both radioactive balls.
XXX Moscow Mathematical Olympiad
M29. n identical coins lie on the table, forming a closed chain (see figure). How many revolutions will a coin M of the same size make during the time it is processed once along the outside of the entire chain, as shown in figure (coin M=2 kopecks)?
How will the answer change if coin M has a radius that is k times different from the radius of each coin in the chain?
M30. Prove that N points on a plane can always be covered by several disjoint circles, the sum of their diameters is less than N and the distance between any two of them is greater than 1. (The distance between two circles is the distance between their closest points.)
V. I. Arpold
MMT
These letters stand for: MOSCOW MATHEMATICAL TECHNIQUE.
Before history, MMT was the only secondary educational institution training specialists in applied mathematics. Since the fall of 1970, training in this specialty will begin in one of the Leningrad and one of the Dnevopotrebsk technical ministries of acquisition, automation equipment and control systems of the USSR.
Duration of study at MMT: for those who have completed the 8th grade of secondary school - 2 years 10 months, and for those who have completed the 10th grade - 1 year 10 months. Those who successfully graduate from technical education receive an exciting and necessary specialty for the national economy - computer mathematician. He can work in computer centers, departments and laboratories at factories, industry associations of computer technology and design bureaus.
But the most important thing is that MMT graduates master mathematical culture in a very high sense of the word.
In 1970, another recruitment took place at MMT. Admission exams in mathematics (oral) and literature (written) will begin on August 1. If you are interested in applied mathematics and would like to receive information about MMT, we provide you with its address:
Moscow E-43, Nizhnyaya Pervomaiskaya, 14, Moscow Mathematical Technical Ministry of Automation Equipment and Control Systems of the USSR, phone: 165-64-72.
Unfortunately, there are no promises for technical demonstrations.