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Triangular sticks


Best Answer CaptainEd, 19 December 2012 - 07:01 PM

Spoiler for Observation about OP--Break once, break both pieces, discard one
Go to the full post


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19 replies to this topic

#1 bonanova

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Posted 24 October 2012 - 07:45 PM

There is a standard problem that asks, if you randomly break a stick into three pieces, the probability that the pieces can form a triangle. The answer is not unique because there are different ways to randomly create three pieces. The method that is the most challenging to analyze breaks the stick at a random point, randomly chooses one of the pieces, and breaks it at a random point. If you can solve that puzzle you may have insight to solve the following variant:

Break a stick at a random point. Break both pieces at random points. Randomly discard one of the pieces. What is the probability the remaining pieces can form a triangle?
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 ~andy~

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Posted 24 October 2012 - 07:55 PM

[Spoiler spoiler=please use spoilers]100%
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#3 hhh3

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Posted 25 October 2012 - 08:42 AM

hmm.. well..
Spoiler for i would say

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alWaYs gaMe!!!

#4 phil1882

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Posted 25 October 2012 - 11:18 AM

if a side is longer than the sum of the other two it doesn't form a triangle.
Spoiler for my guess

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#5 hhh3

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Posted 25 October 2012 - 01:03 PM

oh.. yes.. thanks phil1882... i didnt really think about ""if a side is longer than the sum of the other two it doesn't form a triangle.
"" now it jst bcame a lot more complicated than it first seemed
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alWaYs gaMe!!!

#6 ~andy~

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Posted 25 October 2012 - 03:47 PM

Yes, your'e right Phil, i didn't think of that either, without working it out it has to be less than 25%
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#7 Prof. Templeton

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Posted 25 October 2012 - 04:29 PM

Spoiler for Some thoughts

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#8 CaptainEd

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Posted 26 October 2012 - 08:19 PM

Spoiler for My small simulation results

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#9 bonanova

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Posted 26 October 2012 - 08:21 PM

Hint:

Solve these problems first:
  • Break the stick at two random points.
  • Break the stick at a random point. Break one of the pieces at a random point.
These can be solved in closed form; are they the same?
Verify the answers by simulation if you like.
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#10 bonanova

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Posted 26 October 2012 - 08:26 PM

Spoiler for My small simulation results


That's close, Cap'n.
10x more cases should get you to 3-decimal-place accuracy.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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