Consider n ³ 3 straight lines in general position in the plane: no two lines are parallel and no three lines meet at a common point. How many triangles, T(n), do the lines determine?

The most difficult problem given at the 35th Moscow Mathematical Olympiad in 1972 stated that T(n) ³ 2n/3; the problem was posed for n = 3000.

It turns out that almost 100 years earlier (in 1889), S. Roberts reached the conclusion that T(n) ³ n-2, but his argument is not convincing. The first ``true'' proof was published by R. W. Shannon in 1979, but it is not elementary.

An elementary proof (based on interesting dynamics) was found in 1992 by the Russian mathematician A. Belov-Kanel', who also extended the result to any dimension: if T(n,d) is the number of tetrahedra (simplices) in an arrangement of n hyperplanes in general position in \bold R^d, then T(n,d) ³ n-d.

The talk will be devoted to the solution of the Olympiad problem and Belov's proof.