Orchard Planting Problem

Classic Problem
A given number $n$ of trees are to be planted in an orchard so as to make the number of rows of $k$ trees the largest number possible.

That is:

$n$ points are to be configured in the plane so that the number of straight lines that can be drawn through exactly $k$ of these points is maximised.

Also known as
The orchard planting problem can be seen hyphenated: orchard-planting problem.

It is also known as the orchard problem or tree-planting problem.

Note, however, that there exists another, completely different, orchard problem: the Orchard Visibility Problem, with which this one may be confused.

Also see

 * Orchard Visibility Problem