20091030, 05:34  #1 
"Kyle"
Feb 2005
Somewhere near M52..
1625_{8} Posts 
A Needle on a Crack
A needle 2 inches long is dropped at random onto a floor made with wooden boards 2 inches in width, placed side by side. What is the probability that the needle falls across one of the cracks?
Calculus and very basic statistics required Answer: 2/pi Last fiddled with by Primeinator on 20091030 at 05:34 
20091030, 05:43  #2 
Jul 2003
So Cal
2^{5}·79 Posts 
Ha! You're such a buffon!

20091030, 07:09  #3 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23403_{8} Posts 
Buffonade hasn't even started yet.
In Russian, this classical textbook question sounds even more contraversial than you can imagine: "Какова вероятность что игла пересечет половую щель?" Пол = 1) floor; 2) sex. Pardon my Latin. 
20091030, 09:48  #4 
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
The given answer is only approximately correct.
He has forgotten that there is some probability that the needle will fall "point first" and stick in the floor like a flag pole. Last fiddled with by Wacky on 20091030 at 09:49 
20091030, 09:53  #5 
Nov 2008
2·3^{3}·43 Posts 
Also, I wouldn't suppose there is much probability that the needle will land on the floor at all if this experiment is performed in outer space.

20091030, 10:19  #6 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{4}·5·83 Posts 
[pedant]
"falls across" has not been properly defined. Does the needle have to land on the floor at all? Or just pass over (i.e. cross over, fall across the vertical line extending upwards from the cracks) it on the way down and land somewhere else? What if the needle bounces and comes to rest outside the zone of the floor? Is the floor infinite and perfectly flat? Will the needle roll away because of a strong breeze? Is the geometry of the floor Euclidean? Is there a strong gravity field curving the floor so the needle can't rest on a flat surface? Are there magnets under the floor? Is the needle magnetic and is there a prevailing magnetic field (like on Earth)? What if the needle falls into a crack? Is that considered "across"? If the needle is 2 inches long and 1.9999 inches in diameter then how do you judge "across"? What if the needle is 1.9999 billion light years in diameter? Will the weight of the needle distort the floor? [/pedant] Last fiddled with by retina on 20091030 at 10:29 
20091030, 11:52  #7 
6809 > 6502
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Aug 2003
101×103 Posts
2^{4}×3^{3}×5^{2} Posts 

20091030, 22:51  #8 
"Kyle"
Feb 2005
Somewhere near M52..
917_{10} Posts 
I had not seen this puzzle until a few days ago and found it rather interesting. Although some peculiar caveats have been mentioned... I believe the problem assumes the needle will not plant itself like a flag and is asking the probability of it falling to the floor and then "settling" in a crack. Also, I would assume the diameter of the needle is approximated as being the same as that of the crack.

20091030, 23:56  #9  
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
Quote:
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Given an infinite plane, ruled with uniformly spaced parallel lines, what is the probability that a randomly oriented diameter of a randomly placed circle will intersect one of the ruled lines if the diameter of the circle is the same as the spacing between the ruled lines. Last fiddled with by Wacky on 20091030 at 23:59 Reason: A line is infinite in length. A line segment has a finite length. 

20091031, 00:39  #10  
6809 > 6502
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Aug 2003
101×103 Posts
2^{4}·3^{3}·5^{2} Posts 
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20091031, 16:27  #11  
"Lucan"
Dec 2006
England
2×3×13×83 Posts 
Quote:
between 0 and 90 or 180 David (Pedants please note, I am talking in degrees Fahrenheit down here) A lyric in this classic irritates me: http://www.youtube.com/watch?v=ibINozjZEg 200 degrees that's why they call me "Mr Fahrenheit". I'd be more impressed by "Mr Celsius". Last fiddled with by davieddy on 20091031 at 16:58 

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