Mark,

I've been toiling over this puzzle since the 7th grade back in 1981 when my Algebra teacher gave our class this puzzle and said that there is a solution.  It has continued to haunt me all these years and tonight while sitting at my desk working out an order and waiting for a response to an email question, I once again found myself drawing my nemesis and attempting to complete its elusive solution when I came to the realization (after two unsuccessful attempts) that this puzzle isn't nearly as difficult as I had once imagined...in fact it is quite simple.

The long standing premise has always been that the solution had to be a continuous line that passes through all lines of the puzzle.  The misconception with the puzzle, however, (and I just finally realized this after 28 years) is that the puzzle consists of 16 crossings.  This puzzle actually only has 8 crossings to make...I've been thinking about it completely wrong and now feel really stupid.

Consider this...to draw the puzzle itself we have to draw seven line segments.  We can talk about nodes and such but that only muddies the water and adds to the misconception.  Taken in the simplest form, a line segment exists between two points.  We create those points and segments when we build the puzzle and the nodes do not create additional lines, they only mark a common point of two separate line segments. 

With that, I humbly submit my solution to the masses for consideration and hopefully closure to the ongoing torment that has been this puzzle.  Let me know what you think.

Line Segments crossed
AB
AC
BD
CD
EF
JK
ZL
GH

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