1972 IMO Problems
Problems of the 14th IMO 1972 in Poland.
Problem 1
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.
Problem 2
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.
Problem 3
Let and
be arbitrary non-negative integers. Prove that
is an integer. (
.)
Problem 4
Find all solutions of the system of inequalities
where
are positive real numbers.
Problem 5
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
.
Problem 6
Given four distinct parallel planes, prove that there exists a regular tetrahedron with a vertex on each plane.
- 1962 IMO
- IMO 1962 Problems on the Resources page
- IMO Problems and Solutions, with authors
- Mathematics competition resources
1972 IMO (Problems) • Resources | ||
Preceded by 1971 IMO |
1 • 2 • 3 • 4 • 5 • 6 | Followed by 1973 IMO |
All IMO Problems and Solutions |