From: seghers@hpkslx.mayfield.HP.COM (David Seghers)
Newsgroups: rec.org.mensa
Subject: Nine Dots Solutions!
Date: 25 Jan 93 23:32:37 GMT
Organization: HP Response Center Lab

This post contains the solutions to the "Nine Dot" problem as
published in James L. Adams' "Conceptual Blockbusting," 2nd ed.

Two people sent me the original "right" answer:   Ken Gacioch  and
Vicky Hansen.  Several others had pieces of alternate answers but
hadn't thought them through, and had missed the more obvious 
answer.

OK, for those who are just starting this thread, here's your chance
to do the puzzle before proceeding to the answers.  For the rest,
scroll on down!

Rules:  Connect all nine dots with four or less straight lines
	without lifting your pen. (You know, writing implement! 
	Use blood or graphite if you choose.)


		    *      *      *


		    *      *      *


		    *      *      *








Here's the original solution.


		    1------6------7-------
                    | \                 /
                    |   \             /
		    |     \         /
		    2      5      8
                    |        \   /
		    |          X
                    |        /   \
		    3      4      9
                    |    /
                    |  /
                    |/


Hmmm, there are distinct problems with ASCII graphics.  The word picture
is:  Starting at 1 in the upper left hand corner, draw a vertical line 
down through 2 and 3, and beyond the "boundaries" of the square. 
Then draw the diagonal up and to the right, intersecting 4 then 8 along
this diagonal and again extending beyond the "boundaries" of the square.
Next, draw a horizantal line to the left which interects 7, 6, and 1
of the top row.  Finally, draw a diagonal down and to the right which
intersects 5 and 9. Ta Da!!. Ta Da!!

This puzzle was originally designed to illustrate "thinking outside
the boundaries."  Most people perceive a boundary around the square,
and only when they get past this do they see "the" answer.

Now, here are some of the other solutions which the inventor of the
problem missed to his great embarrassment and edification.  I think
it took a lot to publish the others and use them as examples of the
inventor getting locked into a solution!

  1.  Use big dots and thin lines.  Draw three line at slight diagonals
      in an "N" shape and you pick up all nine dots with three lines.
      This was the officai "smart ass" example.

  2   Use big dots and roll the matrix onto a cylinder.  One spiral
      (straight on the cylinder) line will pick up all dots.

  3.  Fold the paper so that all the dots line up, and draw one
      straight line.  Yes, the paper can be folded that way, and
      in his book he gives you a tear-out page so you can try it! A
      subset of this one is to cut and past the dots into a straight
      line.

  4.  Use a very small matrix, about 1/3 inches square, and a *big*
      (wide) marker.  Draw one line which covers all the dots.  This
      one was submitted by a 10 year old.

  5.  Lay out the matrix on a sphere. One straight (spiral) line will
      catch them all.

  6.  This is a whimsical one, and doesn't necessarily work, but it 
      could...  Cut our all the dots, stack them, and drive the pen
      through the dots.  One line, in a z axis...

These are probably not all!  Can you devise more?

Have Fun!!

David Seghers (seghers@hpcc01.HP.COM) 415-691-3730

************************************************************************
Solipsist Society, Founding Member  (I think, therefore you are.)

Charter member of the "I HATE vi!" Club.
************************************************************************
The statements and opinions above are my own, entirely my own, and no one
else's.

Best Regards,

David Seghers (seghers@hpcc01.HP.COM) 415-691-3730

************************************************************************
Solipsist Society, Founding Member  (I think, therefore you are.)

Charter member of the "I HATE vi!" Club.
************************************************************************
The statements and opinions above are my own, entirely my own, and no one
else's.
Newsgroups: rec.org.mensa