1972 IMO Problems
Problems of the 14th IMO 1972 in Poland.
Prove that from a set of ten distinct two-digit numbers (in the decimal system), it is possible to select two disjoint subsets whose members have the same sum.
Prove that if , every quadrilateral that can be inscribed in a circle can be dissected into quadrilaterals each of which is inscribable in a circle.
Let and be arbitrary non-negative integers. Prove that is an integer. (.)
Find all solutions of the system of inequalities where are positive real numbers.
Let and be real-valued functions defined for all real values of and , and satisfying the equation for all . Prove that if is not identically zero, and if for all , then for all .
Given four distinct parallel planes, prove that there exists a regular tetrahedron with a vertex on each plane.