Problem 613

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Eventhorizon
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Joined: Fri Sep 23, 2011 1:16 am

Problem 613

Post by Eventhorizon » Sun Nov 05, 2017 5:42 pm

Not sure this matters, since it only applies to two points on the perimeter of the triangle, but what happens if the ant lands on the intersection of the hypotenuse and either of the short sides?

There is a range of directions that involve the ant exiting the triangle crossing both the hypotenuse and the short side.

I have difficulty figuring stuff out at limits, so maybe this is not an issue. Perhaps landing on the perimeter means the ant has already crossed? So we only need to worry about points infinitesimally close to the edges of the triangle?

This is a nice question, by the way.

Thanks.
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LilStalker
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Joined: Thu Nov 03, 2016 4:32 pm

Re: Problem 613

Post by LilStalker » Sun Nov 05, 2017 7:39 pm

I can assure you that those things dont matter.
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v6ph1
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Re: Problem 613

Post by v6ph1 » Sun Nov 05, 2017 7:46 pm

The probability of landing exactly at the 3 corners or at one of the three edges is de facto zero.
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MHealy
Posts: 39
Joined: Sat Nov 17, 2012 11:32 pm

Re: Problem 613

Post by MHealy » Mon Nov 06, 2017 12:10 am

Not sure if this is the right place for this, but there are some typos in this problem description: balkony, prepairing and Pythogorean.
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hk
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Location: Haren, Netherlands

Re: Problem 613

Post by hk » Mon Nov 06, 2017 9:03 am

Thanks, fixed (I hope).
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Eventhorizon
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Joined: Fri Sep 23, 2011 1:16 am

Re: Problem 613

Post by Eventhorizon » Fri Nov 17, 2017 1:59 am

Thanks v6ph1 and LilStlker,

Finally got back to the problem and knocked it out in 10 minutes or so!
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ulrich
Posts: 2
Joined: Sun Sep 23, 2012 4:48 pm

Re: Problem 613

Post by ulrich » Mon Jan 08, 2018 6:06 pm

Is this the correct answer format: 0.1234567890 ?

traxex
Posts: 77
Joined: Thu Oct 19, 2017 12:30 pm

Re: Problem 613

Post by traxex » Mon Jan 08, 2018 6:49 pm

Yes.
Technically, everyone is full of himself.

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RishadanPort
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Re: Problem 613

Post by RishadanPort » Tue Aug 20, 2019 3:41 pm

I don't see how the ant could land "exactly" on the edge without also touching the internal area of the triangle.

That would mean that the ant is infinitesimally small, and impossible to see.
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MuthuVeerappanR
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Re: Problem 613

Post by MuthuVeerappanR » Wed Aug 21, 2019 2:55 am

It's just a mathematical description RishadanPort. To make it more abstract, if you randomly select a point inside a right angled triangle and randomly choose some direction to draw a line (starting from the point we chose), what is the probability that the line intersects the hypotenuse?
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