Lines
Source: APMO 1992
March 11, 2006
geometry unsolvedgeometry
Problem Statement
Determine all pairs of positive integers with the following property:
If one draws horizontal lines and another lines which satisfy
(i) they are not horizontal,
(ii) no two of them are parallel,
(iii) no three of the lines are concurrent,
then the number of regions formed by these lines is 1992.