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Topic: A fun problem
Replies: 5   Last Post: Aug 10, 2014 8:55 AM

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Stan Brown

Posts: 1,320
Registered: 12/6/04
A fun problem
Posted: Aug 2, 2014 8:09 AM
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A co-worker's son came up with this one. I was able to find the
answer by a Monte Carlo simulation, but it seems it should be
possible to solve it analytically too.

Place three points randomly anywhere on the perimeter of a square.
All positions are equally likely, and each point is placed
independently. (In particular, there's no assurance that a given
point will or won't fall on the same side of the square as another
point.) What is the probability that the triangle connecting the
three points contains the center of the square?

By Monte Carlo simulation, the answer is ....

(spoiler space)
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(spoiler space)

1/4.


--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com
Shikata ga nai...




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