Problem 613

[Eventhorizon]

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.

[LilStalker]

I can assure you that those things dont matter.

[v6ph1]

The probability of landing exactly at the 3 corners or at one of the three edges is de facto zero.

[MHealy]

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

[hk]

Thanks, fixed (I hope).

[Eventhorizon]

Thanks v6ph1 and LilStlker,

Finally got back to the problem and knocked it out in 10 minutes or so!

[ulrich]

Is this the correct answer format: 0.1234567890 ?

[traxex]

Yes.

[RishadanPort]

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.

[MuthuVeerappanR]

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?