Magic Hexagon

I found this during a terribly terribly boring day at work (before I discovered the light and vowed never to work in an open plan office again).
A lovely little problem.   Can you assign the numbers 1 to 19 to the nodes in the diagram such that the three numbers in every line segment always add up to 22?  I figured it out after about a day (mostly in the office) using logic alone.  But what I couldn't understand is how the problem setter knew a solution would exist?  I posed the question on the site but never got an answer.

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