MathDB

6.1 The bindery had 92 sheets of white paper and

135

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

1

1965

, you get the number, the last whose non-zero digit is even.
6.3 The front tires of a car wear out after

25,000

kilometers, and the rear tires after

15,000

kilometers of travel. When should you swap tires so that they wear out at the same time?
6.4 A rectangle

19

\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

1

49

are written out in table form

\,\,\,1\,\,\,\,\,\, 3\,\,\,\,\,\, 5\,\,\,\,\,\, 7\,\,\,\,\,\, 9

11\,\,\, 13\,\,\, 15\,\,\, 17\,\,\, 19

21\,\,\, 23\,\,\, 25\,\,\, 27\,\,\, 29

31\,\,\, 33\,\,\, 35\,\,\, 37\,\,\, 39

41\,\,\, 43\,\,\, 45\,\,\, 47\,\,\, 49

5

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.

Problem Statement