7.1 Prove that a natural number with an odd number of divisors is a perfect square.
7.2 In a triangle ABC with area S, medians AK and BE are drawn, intersecting at the point O. Find the area of the quadrilateral CKOE.
https://cdn.artofproblemsolving.com/attachments/0/f/9cd32bef4f4459dc2f8f736f7cc9ca07e57d05.png7.3 . The front tires of a car wear out after 25,000 kilometers, and the rear tires after 15,000 kilometers. When you need to swap tires so that the car can travel the longest possible distance with the same tires?
7.4 A 24×60 rectangle is divided by lines parallel to it sides, into unit squares. How many parts will this rectangle be divided into if you also draw a diagonal in it?
7.5 / 8.4 Let [A] denote the largest integer not greater than A. Solve the equation: [(5+6x)/8]=(15x−7)/5 .
7.6 Black paint was sprayed onto a white surface. Prove that there are two points of the same color, the distance between which is 1965 meters.
PS. You should use hide for answers.Collected [url=https://artofproblemsolving.com/community/c3988081_1965_leningrad_math_olympiad]here. leningrad math olympiadalgebrageometrycombinatoricsnumber theory