The 22 dots in the figure below can be connected by 11 lines, each beginning and ending with a dot (o) and passing through 4 empty cells. Connecting lines may proceed horizontally or vertically, but not diagonally. They may change direction as often as needed, and they should not cross one another.

               +---+---+---+---+---+---+---+---+
               |   | o | o |   |   | o |   | o |
           +---+---+---+---+---+---+---+---+---+---+
           |   |   | o | o | o |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+---+---+
           |   |   |   |   |   | o |   |   |   | o |
           +---+---+---+---+---+---+---+---+---+---+
           | o |   |   |   |   |   |   | o |   | o |
           +---+---+---+---+---+---+---+---+---+---+
           | o |   |   | o |   |   | o | o |   |   |
           +---+---+---+---+---+---+---+---+---+---+
           | o |   |   | o |   | o |   |   |   |   |
           +---+---+---+---+---+---+---+---+---+---+
               |   |   | o |   |   |   | o | o | 
               +---+---+---+---+---+---+---+---+

Can you do it?

Method:
I pasted onto ms paint and started drawing lines.  Lots of logic and deduction is involved.  There were some patterns that I used to my advantage.  Every empty space must connect to exactly two adjacent spaces, for one.  That means those two empty spaces in the upper left corners must each connect to the south and east.

Solution:
This is how my ending picture looked:

   _. .___  .  _.
 _| . . . |_| |  _
|  _| | | .___    !
! |  _| |_____. |_.
._| |_.  ___. .___
._   _. | .  _   _|
  |_| ._| |_| ! !

It may not be clear from the unclear picture, but in the upper right corner, I left open a little space.  There are four points that have not yet been matched there.  I can either match points A with B and C with D, or I can match A with C and B with D.  I may have missed something, but it appears these are two distinct solutions.

Posted by Tristan on 2005-08-16 02:38:00