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Hi;

You can divide by 2 or multiply by 1 / 2. Welcome to the forum.

Hi;

Welcome to the forum.

That would be a piece of luck. M exposes all my weaknesses.

Hi;

Thanks for the link. I understand how you want to count them say for ()()(). But what is the question you are asking?

I do see the formula you are conjecturing on page 5 of that pdf.

Hi;

I think I understand the problem now. I have notes on this bracketing problem somewhere. I am looking for them now.

Hi;

I do not understand about R(t), L(t), can you explain further.

The numbers you are suggesting are every other Catalan number.

Hi;

The solutions found in post #10 are correct but I am afraid their might be more that ht method I used there is missing. I hate using reasoning in math, that is why I dislike and mistrust the whole concept of proof. Trouble is, computation although more reliable can leave you hanging.

It is very desirable to get an analytic form. Can you do that, with the same rules still applying?

Hi chamywak;

The number they want next is

.Welcome to the forum.

Those were just thoughts, that might have a big hole in it.

There is undoubtedly a much shorter way to do this.

This will be the toughest baffler ever posed here.

Disclaimer: Do not try this problem and then drive or operate heavy machinery.

Okay, you see that side PQ is the square root of 3 and the equation of the ellipse is given below it.

The rules are rather extreme:

You may not use any CAS, that means Mathematica, Maxima, Wolfram Alpha, Maple, Matlab, Mupad, Octave, Pari, Yacas, Fricas, Magma.

You may not use any programming language, that means C, C++, Wolfram, Haskell, Basic, Pascal, Cobol, Fortran, Python or any other.

You may not use any mathematics that means calculus, group theory, algebra, trigonometry, geometry (Euclidean or any other), probability, any math theorem.

You can only use the tools of EM or you can try the force.

Okay, now for the question:

If we move P and Q along the circumference of that ellipse what is the sum of the largest area and the smallest area for triangle POQ? Of course the length of PQ must always remain constant at

A says) 2.

B says) That is not correct.

C says) 6.022 x 10^23

D says) 0

E says) I know the answer.

Yes, Length is the command that will tell you how long that list is. You can try this.

```
Select[Range[10000], PrimeQ[#^2 + 27] && PrimeQ[# + 3] &];
Total[%]
Length[%%]
```

Have a good lunch.

Hi;

For a functional approach:

`Select[Range[10000], PrimeQ[#^2 + 27] && PrimeQ[# + 3] &] // Total`

We can say that

Solving simultaneously:

{{x = -5, y = -3}, {x = -5, y = 3}, {x = 5, y = -3}, {x = 5, y = 3}}

Are the only 4 solutions and they all give n = 13.

Very good work!

Since the limit of -x^2 as x approaches 0 is 0 and the limit of x^2 as x approaches 0 is 0 and

stays between them, the limit of it as x approaches 0 is also 0.Intuitively we can understand by the following drawing that Mathegocart provided:

If your function the green line always stays between the red and the blue line, then as the red and the blue line get closer together the green line gets sandwiched in between.

What do you not understand?

Hi;

I like them too...Is there some question you have about them?

Hi;

Because of the substitution in post #2.

What makes you think there are more?

Hi;

n = 13 can be found quickly.