Nicely done, Channel 9 (posted by Dr Herbie).

giovanni said:

CreamFilling512 said:

*snip*

That was easy! Your solution is much faster than mine! Excel is not the best tool for this kind of problems, but I didn't have anything handy at the office.

 

Still not sure what the first equation meant...

This is my naive solution to the second problem, it approaches 9 as k approaches infinity.

static void Main(string[] args) { 
    Func<double, double> f = (k) => (Math.Pow((1 + (1 / k)), 3)) / (1 + (3 / k)); 
    double z = f(1); 
    for (double k = 2; k < double.MaxValue; k++) { 
        z *= f(k);
        Console.WriteLine(3 + z);
    } 
}

Completely wasn't thinking of what day it was ... nice job Charles and co.!

I viewed the page source, got the URL for this thread.... Nice and simple.

brianbec said:

CreamFilling512 said:

*snip*

Now, for a little secret: type the same thing into Wolfram Alpha, just replacing "3" with "n" (and, for even more secrets, leave off the first "n + " -- just type in the big infinite product

The second problem is n + the gamma function, Γ(n+1), with n = 3.

Here's a graph of the absolute value of the Gamma function on the complex plane, from Wikipedia:

W3bbo said:

Sven Groot said:

*snip*

I got it, but only by coincidence: I had a series of classes on lambda calculus last week and I recognised the Church encoding of the natural numbers as lambda functions (as contextfree said). Simply count the level of recursion to get the number, in this case it was 9-deep, so it represents '9'.

 

I recognised the other question as product notation. Going by the frequent use of '3' and how 3*3 == 9 I figured the answer was the same.

 

Note that I actually advocate implementing something similar to this as an actual captcha in future. Keep it just as difficult, I like the idea of there being a forum with just me on it

Actually that was 3+product()

JoshuaAllen said:

giovanni said:

*snip*

@giovanni -- the first formula was the easiest: just count the f's! 

Yes, it is easy once you know what the notation mean

I just did a Google search on λf.λx.f(x and got the wiki entry on Church notation.

Before that, I tried just entering random things a couple of times to see if it would eventually let you in. After 9 times of entering bad answers you get a subtle hint.

yey! I passed.

Richard.Hein said:

giovanni said:

*snip*

This is my naive solution to the second problem, it approaches 9 as k approaches infinity.

 

static void Main(string[] args) { 
    Func<double, double> f = (k) => (Math.Pow((1 + (1 / k)), 3)) / (1 + (3 / k)); 
    double z = f(1); 
    for (double k = 2; k < double.MaxValue; k++) { 
        z *= f(k);
        Console.WriteLine(3 + z);
    } 
}

I did it with PowerShell.  Anyway, way to go Channel9!

Ion Todirel said:

mastermine said:

*snip*

I didn't bother to look, I was like "knowing the C9 devs they probably did server side validation"

http://www.wolframalpha.com/input/?i=product+of+((1+%2B+1/k)^3+/+(1+%2B+3/k))+for+k+%3D+1+to+inf">http://www.wolframalpha.com/input/?i=product+of+((1+%2B+1/k)^3+/+(1+%2B+3/k))+for+k+%3D+1+to+inf

http://www.wolframalpha.com/input/?i=product+of+((1+%2B+1/k)^3+/+(1+%2B+3/k))+for+k+%3D+1+to+inf">

Although I solved it by counting the number of f's in the first formula, then realizing that the number '9' was special to C9.