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

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-) |

Guest Message by DevFuse

Started by bonanova, Oct 24 2012 07:45 PM

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
19 replies to this topic

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?

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?

*Vidi vici veni.*

Posted 24 October 2012 - 07:55 PM

[Spoiler spoiler=please use spoilers]100%

Posted 25 October 2012 - 08:42 AM

hmm.. well..

Spoiler for i would say

alWaYs gaMe!!!

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

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

"" now it jst bcame a lot more complicated than it first seemed

alWaYs gaMe!!!

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%

Posted 25 October 2012 - 04:29 PM

Spoiler for Some thoughts

Posted 26 October 2012 - 08:19 PM

Spoiler for My small simulation results

Posted 26 October 2012 - 08:21 PM

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.

Verify the answers by simulation if you like.

*Vidi vici veni.*

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.

*Vidi vici veni.*

0 members, 0 guests, 0 anonymous users