Problem 296

[Quique12]

In problem 296, if it would be the case that a triangle could have two ways of having BE integral (say for example that if you rotate the labels A,B,C the "new triangle" would have a different BE if the triangle is not equilateral). Do these count as two different triangles?

[jaap]

You can't rotate the labels, as it is specified in the problem that AB is the longest side and BC the shortest.

[Quique12]

Thanks jaap.
It simplifies the problem a little as I don't have to check 6 permutations for the labels. I noticed that most of the time BE is integral is when BC<= AC<=AB anyways. I wonder if there's a good reason for that.

[Quique12]

After two days running my computer gave me the wrong answer. I want to know if the algorithm is completely wrong. So I'll post what I have if the perimeter were up to 1000 and ask if someone can confirm. Hopefully that is not too spoilery.
My answer for 1000 would be: 190

[ThomasH]

My answer for 1000 would be: 190

That is not even in the neighbourhood of the correct value.

[Quique12]

I found the mistake in the program. I later wrote another one and got the correct answer in 2.5 hours of running time. My algorithm seems to be the same as the algorithm used by the first posters but somehow in Mathematica it runs in 2.5 hours and it ran much quicker on their programming languages.

[nicolas.patrois]

Is the answer for 1000 is 492574?

[Marcus_Andrews]

No -- too high.

[nicolas.patrois]

Is p=100000 is accepted? Of course.
I think that I found my error.