You can connect them without leaving the rectangle in four straight lines.

Suppose the rectangle is

A B C
D E F
G H I

The solution is A->B-C->F->E->D->E->F->I->H->G.

Note that you can draw this without leaving the hand from the paper, but you have to draw on the line DEF twice. But the result is four straight lines.

Xinding Sun

Thank you.

This is a very nice observation, although it violates the unspoken rules. However, in so far as the rules are only implicit, your procedure gives a working example of a benefit drawn from switching a view point. I'll have this incorporated into my page.

Happy New Year,
Alexander Bogomolny