An

old chestnut goes like this:

Take a 3-by-3 grid of evenly-spaced points, like the one below:

. . .
. . .
. . .

On a piece of paper, draw 4 straight lines
without lifting your pencil from the paper
in such a way that they go through all 9 points.

Note that it's easy to do this with 5 lines: make three of them
horizontal and going through 3 points each, and use the other two
to connect them. But you need to do it with only 4 lines.

There are variations of this puzzle for larger grids. In general, it is possible to solve the NxN grid in 2N-2 lines.

Answer

An extension of this problem appears at http://www.mathpuzzle.com/dots.html . It's on the later part of that page; a different connecting-dots problem is at the top.

Connect a 3x4 grid of points with 5 continuous lines, ending where you started, and without crossing any point twice.

Connect a 4x4 grid of points with 6 continuous lines, ending where you started, and without crossing any point twice.

etc.