7.1. Prove that from the sides of an arbitrary quadrilateral you can fold a trapezoid.
7.2 / 6.2 The numbers A and B are relatively prime. What common divisors can have the numbers A+B and A−B?
7.3. / 6.4 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.
7.4 In a six-digit number that is divisible by 7, the last digit has been moved to the beginning. Prove that the resulting number is also divisible at 7.
[url=https://artofproblemsolving.com/community/c6h3391057p32066818]7.5* (asterisk problems in separate posts)
7.6 On sides AB and BC of triangle ABC , are constructed squares ABDE and BCKL with centers O1 and O2. M1 and M2 are midpoints of segments DL and AC. Prove that O1M1O2M2 is a square.
https://cdn.artofproblemsolving.com/attachments/8/1/8aa816a84c5ac9de78b396096cf718063de390.pngPS. You should use hide for answers.Collected [url=https://artofproblemsolving.com/community/c3983459_1962_leningrad_math_olympiad]here. geometryalgebracombinatoricsnumber theoryleningrad math olympiad