## Problem 613

A place to air possible concerns or difficulties in understanding ProjectEuler problems. This forum is not meant to publish solutions. This forum is NOT meant to discuss solution methods or giving hints how a problem can be solved.
Forum rules
As your posts will be visible to the general public you
are requested to be thoughtful in not posting anything
that might explicitly give away how to solve a particular problem.

This forum is NOT meant to discuss solution methods for a problem.

In particular don't post any code fragments or results.

Don't start begging others to give partial answers to problems

Don't ask for hints how to solve a problem

Don't start a new topic for a problem if there already exists one

Don't post any spoilers
Comments, questions and clarifications about PE problems.
Eventhorizon
Posts: 19
Joined: Fri Sep 23, 2011 1:16 am

### Problem 613

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
Posts: 64
Joined: Thu Nov 03, 2016 4:32 pm

### Re: Problem 613

I can assure you that those things dont matter.

v6ph1
Posts: 119
Joined: Mon Aug 25, 2014 6:14 pm

### Re: Problem 613

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

MHealy
Posts: 39
Joined: Sat Nov 17, 2012 11:32 pm

### Re: Problem 613

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

hk
Posts: 10638
Joined: Sun Mar 26, 2006 9:34 am
Location: Haren, Netherlands

### Re: Problem 613

Thanks, fixed (I hope).

Eventhorizon
Posts: 19
Joined: Fri Sep 23, 2011 1:16 am

### Re: Problem 613

Thanks v6ph1 and LilStlker,

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

ulrich
Posts: 2
Joined: Sun Sep 23, 2012 4:48 pm

### Re: Problem 613

Is this the correct answer format: 0.1234567890 ?

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

### Re: Problem 613

Yes.
Technically, everyone is full of himself.

Posts: 78
Joined: Mon Jun 10, 2013 6:31 am

### Re: Problem 613

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.

Rishada is the gateway to free trade—but the key will cost you.

MuthuVeerappanR
Posts: 419
Joined: Sun Mar 22, 2015 2:30 pm
Location: India
Contact:

### Re: Problem 613

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?

It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.