MathDB

6.1 Three people with one double seater motorbike simultaneously headed from city A to city B . How should they act so that time, for which the last of them will get to , was the smallest? Determine this time. Pedestrian speed - 5 km/h, motorcycle speed - 45 km/h, distance from A to B is equal to 60 kilometers .
6.2 / 7.2 The numbers

A

and

B

are relatively prime. What common divisors can have the numbers

A+B

and

A-B

?
6.3. A person's age in

1962

was one more than the sum of digits of the year of his birth. How old is he?
6.4. / 7.3

15

magazines lie on the table, completely covering it. Prove that it is possible to remove eight of them so that the remaining magz cover at least

7/15

of the table area.
6.5. Prove that a

201 \times 201

chessboard can be bypassed by moving a chess knight, visiting each square exactly once.
6.6. Can an integer whose last two digits are odd be the square of another integer?
PS. You should use hide for answers.Collected [url=https://artofproblemsolving.com/community/c3983459_1962_leningrad_math_olympiad]here.

Problem Statement