# SPUG: Stick Riddle

SPUG-list-owner tim at consultix-inc.com
Thu Jan 2 21:21:54 CST 2003

```On Thu, Jan 02, 2003 at 06:33:07PM -0800, Don Shanks wrote:
> Am I missing something, or do three sticks joined end to end always make
> a triangle?

I puzzled over this early on myself, because the way the problem was
phrased, it could have been interpreted as "will the three sticks form a
triangle -- or would it be some other geometric shape?"  (as if!).
And that distracted me from the real issue, which is one of "gap-bridging".

Let's cast fancy formulas aside for the moment and just imagine
the spatial requirements:  if you had one long stick and two
shorter ones, you could join two ends together, but perhaps be unable to
bridge the gap between the others.

For example:

----------------------	#1
\
\
#2

And here's stick #3:  --

Unfortunately, #3 is too short to simultaneously touch the ends
of both of the others to enclose a common area, and therefore we ain't
got no triangle.

Or, to approach it from Yet Another Angle, what we've got instead of a
triangle is, in air travel parlance, an Open Jaw Itinerary, instead of
a Circle one.

-Tim
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