# SPUG: Stick Riddle

Geoffrey & Kristin Grosenbach glyph at mac.com
Wed Jan 1 18:30:48 CST 2003

```During a new year's party last night, a friend who is finishing a
master's degree in applied math gave me a riddle (of sorts).

THE PROBLEM:

Take a stick and randomly split it into three pieces. What is the
probability that the three pieces will be able to make a triangle?

(HINT: Three lengths make a triangle if the longest piece is shorter
than the sum of the other two).

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THE SOLUTION:

In his college course, he came up with the answer of 50% probability. I
wrote the attached Perl script to simulate this, and constently get 38%,
assuming the second split is done on the larger piece.

It appears that rand() is consistently random enough to give good
results, so that's not an issue. Should I tell him he's wrong (and use
Perl to prove it), or am I making an obvious error?

Geoff

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