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: 5

1986 Tournament Of Towns, (128) 3
Tags: cover , triangle , combinatorics , combinatorial geometry
Does there exist a set of $100$ triangles in which not one of the triangles can be covered by the other $99$?

1985 Tournament Of Towns, (095) 4
Tags: cover , geometry , convex , circles , combinatorial geometry
The convex set $F$ does not cover a semi-circle of radius $R$. Is it possible that two sets, congruent to $F$, cover the circle of radius $R$ ? What if $F$ is not convex? ( N . B . Vasiliev , A. G . Samosvat)

1988 Tournament Of Towns, (172) 5
Tags: circles , combinatorics , combinatorial geometry , cover
Is it possible to cover a plane with circles in such a way that exactly $1988$ circles pass through each point? ( N . Vasiliev)

1987 Tournament Of Towns, (145) 2
Tags: combinatorial geometry , cover , disc , distance
Α disk of radius $1$ is covered by seven identical disks. Prove that their radii are not less than $\frac12$ .

2013 Argentina National Olympiad Level 2, 6
Tags: square , geometry , rectangle , cover
Is there a square with side lenght $\ell < 1$ that can completely cover any rectangle of diagonal $1$?