This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 4

1968 All Soviet Union Mathematical Olympiad, 094
Given an octagon with the equal angles. The lengths of all the sides are integers. Prove that the opposite sides are equal in pairs. [u]alternate wording[/u] Consider an octagon with equal angles and with rational sides. Prove that it has a center of symmetry.
equal angles integer sides geometry

1936 Moscow Mathematical Olympiad, 029
The lengths of a rectangle’s sides and of its diagonal are integers. Prove that the area of the rectangle is an integer multiple of $12$.
area rectangle integer sides geometry

1991 All Soviet Union Mathematical Olympiad, 537
Four lines in the plane intersect in six points. Each line is thus divided into two segments and two rays. Is it possible for the eight segments to have lengths $1, 2, 3, ... , 8$? Can the lengths of the eight segments be eight distinct integers?
integer sides combinatorial geometry line

2000 Tournament Of Towns, 2
Two parallel sides of a quadrilateral have integer lengths. Prove that this quadrilateral can be cut into congruent triangles. (A Shapovalov)
integer sides congruent triangles geometry parallelogram number theory