Rafael Almeida almeidaraf at gmail.com
Sun Jan 13 07:43:52 EST 2008

```On Sun, 13 Jan 2008 11:48:09 +0100, "Nicu Ionita" <nionita at lycos.de> wrote:
>
> Hi Rafael,
>
> I have just two ideas, that could improve your strategy to reduce the
> computation time:
>
> 1. perhaps there is also a minimum (not only a maximul) for the values you
> should try

Yeah, that's a good one, the most I can narrow down the results the better. But
if I can figure out the number of triangles without actually constructing them
would be the real winner algorithm.

> 2. is the function howManyTriangles monotone? If yes, then you could try to
> solve:
>
> howManyTriangles n = 47547
>
> by finding an upper n, nmax, where howManyTriangles nmax > 47547, and than
> using Euler to reduce the interval (from 12 to nmax, then probably from (12
> + nmax)/2 to nmax, a.s.o)
>
> Then you will have ~ ln nmax computations of the function, which could be
> better than computing it from 1 to ...

I wish it was monotone, but it doesn't seem to be anything, I even plotted the
relation cathetus size x number of triangles, but it didn't really show any
pattern. It seems there are more likely results, but there are a few of them
that looks just random. If you want to see the plotted graph:

http://homepages.dcc.ufmg.br/~rafaelc/problem176.png
```