Expert: Rohit Agarwal - 8/5/2007

Question
I've been struggling with this one since taking a statistics course in University in 1976.  I'll try to draw the puzzle as it was presented to me:

         *   *

     *   *   *   *

     *   *   *   *

         *   *

The challenge is this:
Join all of the dots along the horizontal, vertical and diagonals (resulting in an image looking something like 5 envelopes adjacent to each other) without retracing any line, by using just five continuous lines.  I hope I've explained that adequately.  The resulting image is like this:

   *--*
   !\ /!
   !/ \!
*--*--*--*
!\ /!\ /!\ /!
!/ \!/ \!/ \!
*--*--*--*
   !\ /!
   !/ \!
   *--*
Not very good, but the best I can do with the typeface.  I think you'll get the idea.  I've been "doodling with this for over 30 years and can always do it with 6 lines, but have only (I think) done it a couple of times with 5 (maybe I was dreaming?)

Was I dreaming, or is it actually possible??
Regards,
Jim

!/ \!

!/ \!


Answer
I don't know if I've understood your question properly or not. But in case I have, then I have a solution.

First lets assign a variable to each of the dots to help us communicate better.

   a b
 c d e f
 g h i j
   k l

line 1 - from c to just right of f (covers c,d,e,f)
line 2 - from just right of f to below k (covers j,l)
line 3 - from below k to above a (covers k,h,d,a)
line 4 - from above a to just right of j (covers b,f)
line 5 - from just right of j to g (covers j,i,h,g)

In case this is not what you are looking then please don't hesitate to post again.
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