MathDB

6.1 Two people went from point A to point B. The first one walked along highway at a speed of 5 km/h, and the second along a path at a speed of 4 km/h. The first of them arrived at point B an hour later and traveled 6 kilometers more. Find the distance from A to B along the highway.
6.2. A pedestrian walks along the highway at a speed of 5 km/hour. Along this highway in both directions at the same speed Buses run, meeting every 5 minutes. At 12 o'clock the pedestrian noticed that the buses met near him and, Continuing to walk, he began to count those oncoming and overtaking buses. At 2 p.m., buses met near him again. It turned out that during this time the pedestrian encountered 4 buses more than overtook him. Find the speed of the bus
6.3. Prove that the difference

43^{43} - 17^{17}

is divisible by

10

.
6.4. Two squares are cut out of the chessboard on the border of the board. When is it possible and when is it not possible to cover with the remaining squares of the board? shapes of the view without overlay?
6.5. The distance from city A to city B (by air) is 30 kilometers, from B to C - 80 kilometers, from C to D - 236 kilometers, from D to E - 86 kilometers, from E to A- 40 kilometers. Find the distance from E to C.
6.6. Is it possible to write down the numbers from

1

1963

in a series so that any two adjacent numbers and any two numbers located one after the other were mutually prime?
PS. You should use hide for answers.Collected [url=https://artofproblemsolving.com/community/c3983460_1963_leningrad_math_olympiad]here.

Problem Statement