SPUG: Stick Riddle

[Jeremy Calvert]

> Although if A + B = C you have a degenerate triangle
> (basically, they
> "add up" to a straight line).

Fortunately the probability of this happening is 0 and
doesn't affect one's answer, regardless of
(reasonable) interpretation of problem.

I'm interested in understanding why Damian's second
interpretation -in which a break is made randomly
somewhere on the stick, then one of the resulting
sticks is chosen at random and is broken at a randomly
chosen spot- has about a 19% chance of achieving
triangle.  Intuitively, this precise probability is
25% * (1/2 + 1/4) = 18.75%, where the two phase
approach introduces a 50% liklihood of failure in the
second step, but I can't find a way to express this
rigorously.  If you think you have a proof, I'd like
to see it.

J

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