SPUG: The Stick Riddle, with a Twist

Yitzchak Scott-Thoennes sthoenna at efn.org
Fri Jan 3 14:09:50 CST 2003

On 02 Jan 2003 22:41:09 -0800, creede at penguinsinthenight.com wrote:
>On a similar subject, Isaac Asimov recounted a story from (I believe)
>his undergraduate years when he was sitting in on a class with a friend.
>The professor was trying to make a point about breaking a piece of chalk
>in half. The proto-Good Doctor said it couldn't be done, whereupon the
>instructor broke the piece of chalk.
>"That's not it," Asimov said (I'm paraphrasing, because this is all from
>memory). "You now have two whole pieces of chalk." The class laughed.
>"And even if you do have a standard measure for a piece of chalk, how do
>you know whether you've really broken it in half? What if the pieces are
>.51 and .49 of a piece of chalk? What about the dust?"
>For this observation he was kicked out of the class. :)
>The moral of this story is . . . um, always properly define your
>problem. I think. Or maybe it's don't try to one-up the instructor when
>you're in a strange class.

This misses the point of the story.  IIRC, the professor was asserting that
mathemeticians are mystics since they believe in the square root of -1.
Asimov was defending mathemeticians by pointing out the equal "unreality"
of 1/2.

To return to the topic at hand, here's a new twist on the stick riddle:

Assume the stick is an even number of units "L" long (for L >= 3).
Break the stick into 3 sections (each an integral number >= 1 of units
long).  What percentage of possible combinations make a valid triangle
(considering invalid the degenerate A+B=C case).  How about
permutations?  What is the limit of the percentage as L approaches
infinity?  (For both combinations and permutations.)

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