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grade 6

Part of 1965 Leningrad Math Olympiad

Problems(1)

1965 Leningrad Math Olympiad - Grade 6

Source:

8/30/2024
6.1 The bindery had 92 sheets of white paper and 135135 sheets of colored paper. It took a sheet of white paper to bind each book. and a sheet of colored paper. After binding several books of white Paper turned out to be half as much as the colored one. How many books were bound?
6.2 Prove that if you multiply all the integers from 11 to 19651965, you get the number, the last whose non-zero digit is even.
6.3 The front tires of a car wear out after 25,00025,000 kilometers, and the rear tires after 15,00015,000 kilometers of travel. When should you swap tires so that they wear out at the same time?
6.4 A rectangle 1919 cm ×65\times 65 cm is divided by straight lines parallel to its sides into squares with side 1 cm. How many parts will this rectangle be divided into if you also draw a diagonal in it?
6.5 Find the dividend, divisor and quotient in the example: https://cdn.artofproblemsolving.com/attachments/2/e/de053e7e11e712305a89d3b9e78ac0901dc775.png
6.6 Odd numbers from 11 to 4949 are written out in table form    1      3      5      7      9\,\,\,1\,\,\,\,\,\, 3\,\,\,\,\,\, 5\,\,\,\,\,\, 7\,\,\,\,\,\, 9 11   13   15   17   1911\,\,\, 13\,\,\, 15\,\,\, 17\,\,\, 19 21   23   25   27   2921\,\,\, 23\,\,\, 25\,\,\, 27\,\,\, 29 31   33   35   37   3931\,\,\, 33\,\,\, 35\,\,\, 37\,\,\, 39 41   43   45   47   4941\,\,\, 43\,\,\, 45\,\,\, 47\,\,\, 49 55 numbers are selected, any two of which are not on the same line or in one column. What is their sum?
PS. You should use hide for answers.Collected [url=https://artofproblemsolving.com/community/c3988081_1965_leningrad_math_olympiad]here.
leningrad math olympiadalgebranumber theorycombinatoricsgeometry