Forum of Astronomers and Surveyors

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FORUM OF ASTRONOMERS AND GEODESISTS

Six November days (XI. 23-28, 1970) in the assembly hall of Kazan State University. V. I. Ulyanov (Lenin) held the next V Congress of the All-Union Astronomical and Geodetic Society (VAGO) at the USSR Academy of Sciences.

VAGO is a voluntary scientific and public organization engaged in work in the field of astronomy, geodesy and cartography. It was created in 1932. The Society includes 55 branches, uniting 5,640 detective members, 197 collective members (enterprises, institutions, etc.) and 1,040 members of the youth section.

More than 600 people from all over the country took part in the work of the V VAGO Congress. At the congress, organizational issues were considered (report of the Central Council, elections of the governing bodies of the Society and decision-making). At the plenary sessions and sections, scientific reports and messages from the country’s most prominent scientists and amateur astronomers were heard.

At the youth section of the congress, messages from S. S. Voikov, V. V. Martynenko, B. G. Pshenicher, V. V. Chistyakov, S. S. Novikov and others spoke in detail about the work carried out by the members of this section. According to the VAGO Charter, members of the youth section have the right:

“a) participate with a full voice in congresses, conferences, SSSYAH, meetings and meetings of the Society;

b) use the services, laboratories, library, archives and collections of the Society;

b) wear the badge of a member of the Society,”*)

During the period between the IV and V WAGO congresses, members of the youth section, who worked at the 31st branch of the Society, took an active part in amateur scientific work on the study of variable stars, observations of the Sun, service clouds, meteors, artificial Earth satellites, planets, in atmospheric sounding, maintenance of crater-like structures, in the study of crater-like structures - a set of atmospheric phenomena that limit the effectiveness of large telexcopes. In the youth sections of the Moscow, Novosibirsk and Crimean branches of the Society and in the Uglich branch of the Yaroslavl branch, electron meters, photographic cameras, and electron meters were designed and manufactured. In the Crimean and Azerbaijan sections, young astronomers are very successful in amateur telex construction and produce mirrors for amateur astronomers in other cities.

Much attention is paid to organizing various astronomical excursions for schoolchildren. Meteorological expeditions organized in Crimea are regularly held

*) Admission to membership in youth sections will be carried out by branches of the society or their filpals on the basis of a written application from an incoming member of VAGO or an educational institution, enterprise or Komsomol organization.

(For ending see page 21)

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of the previous problem there is a number ending in $n$ zeros.

18. Prove that there is a power of 29 ending in 00001.

19. Let the number $A$ not be divisible by 2 and 5. Prove that for any $n$ there is a power of the number $A$, which when divided by $10^n$ gives a remainder of 1.

20. Prove that there is a multiple of 1970 whose decimal notation contains only ones and zeros.

Table

The table contains $n \times n$ cells containing integers from 1 to $n^2$. You will be interested in the following statement:

“For any arrangement, there are two cells that have a common side such that the difference between the numbers in these cells is greater than 5.”

21. Prove this statement
    a) for $n=10$;
    b) for all $n$, greater than 10;
    c) for $n=9$.

22. Roll it over for $n=5$.

The author does not know whether the statement under consideration is true for $n=6, 7, 8$.

Exercise

23. There are 123 residents in the house; together they are 3813 years old. Is it possible to choose 100 of them that together are at least 3100 years old?

24. There are 7 lines on the data plane, no two of which are parallel. Prove that there are two of them such that the angle between them is less than $26^\circ$. Is the analgetic statement true if $26^\circ$ is replaced by $25^\circ$?

25. Prove that any tree can be cut off $8/15$ of its leaves, leaving at least $7/15$ of the shadow provided by the tree (neglect the shadow from the trunk and branches; the number of leaves can be considered divisible by 15).

26. Twenty-one boys were given 200 nuts. Prove that, no matter how they divide them, there will be two boys who get an equal number of nuts (maybe 0 nuts each).

27. 7 segments are given. The length of each is more than 10 cm and less than 1 m. Prove that any three can form a triangle.

28. From the series 1, 2, …, 200, the 101st number was somehow selected. Prove that one of the chosen numbers is divisible by another.

(End. See page 16 for beginning.)

for young astronomers coming from different places of the USSR. Many members of the junior section were active participants in observing the 1968 solar eclipse.

In recent years, the network of youth astronomical societies and various clubs and groups, uniting about 3,000 schoolchildren, has noticeably expanded. Assistance to these organizations is provided from five regional methodological centers located in the astronomy departments of the Moscow and Baku Pioneer Palaces, in the general school of the Alma-Ata Pioneer Palace, the Crimean region youth general school (Simferopol) and the children’s general school of the Young Technicians Club of the Siberian Branch of the USSR Academy of Sciences, which direct the work of young astronomers to the development of observations using modern methods and technical funds for the design and manufacture of various astronomical instruments and the organization of public schools and astronomical laboratories.

Great attention to the work of young astronomers from the Ministry of Education of the USSR and the RSFSR, the Central Committee of the Komsomol, the Central Station of Young Technicians, VDNKh and the Board of the All-Union Society “Znanie” should be able to develop the work of youth sections of VAGO. All this allowed the First All-Union Conference of Young Astronomy Amateurs to be held in Baku in 1969, which contributed to the exchange and dissemination of the best work of the youth sections of VAGO.

Vice-President of VAGO Professor L. S. Khrenov