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But you are not telling me how to.

I have the same idea but why?

Oh?

I learned that I am 14

anonimnystefy wrote:

Hi bobbym

The y-coordinate of C needs to be pi/2, though, not the x coordinate.

That is what I mean, exactly.

How do I get the coordinates of that rectangl ?

If I know the coordinates of C, yes

Can you explain what this means?

I still do not get it

How do I go there?

I would be needing to figure out the area between the y-axis and the curve.

The answer is "We do not know so far."

Or, here is a longer answer:

1) Can any problem be done without a computer?

This is actually a bad question: mainly because you're not defining a computer rigorously enough. So, instead you could ask:

2) If a problem looks trivial enough, can it be done by means of an average brain, a paper and a pencil and reasonable time?

An well known way to ask this question is If the solution can be verified easily, can the problem be done easily?. No one has solved this question till date.

But triviality is in the eye of the beholder. For example, there are many unsolved problems in number theory (Goldbach's anyone?) which at the first glance looks like were asked by a child; no one has solved them till date.

Textbook problems are designed to test whether you're able to apply the mathematics that you've been taught so far. Hence, the solution is already known even before the problem is framed. That is why they always have solutions. In the real world, we make answers to match the problems, not the other way round.

3) Is there a closed form formula for an m x n board?

I do not know. Maybe someone does, but most likely not. However, not being able to find out a closed form solution is not that bad.

It can indeed be proven (rigorously enough) that not all integer sequences have closed form formulae. The reason being there are an uncountably infinite number of sequences, but only a countably infinite number of closed form formulae.

By the way, there are problems that not even a computer can solve. (Look up halting problem)

4) Does that mean I should give up hope?

Not at all. More than trying to find a closed form expression, try searching for a smarter algorithm that solves the problem, whether by a computer or not. Of course, mathematics will be very useful in doing so.

Also, that does not mean you should give up on trying to find nice results and patterns. Even if there isn't one, it is a challenging task to prove why.

But these are two undeniable realities from the world of the abstract:

a) There is no shame in using a computer

b) Not everything would turn out to be a nice formula or a result in the end.

Oh.

What is her opinion on my solution?

No, I cannot. What is the numerical answer coming to?

zetafunc wrote:

There are two ways to do this problem: geometrically or algebraically. (The former will give you a better idea of what's going on.)

For a geometric approach, try plotting a graph of your function and looking at which parts of the picture correspond to which integrals -- in particular, the area for your inverse function.

For an algebraic approach, make a substitution like x = f(t).

That does not help because if I brought in t, I'd have to change the limits of integration. Can you show me how to do it?

You're welcome!

I only posted an example as a matrix. It is done with LaTeX.

```
[math]
\begin{bmatrix}
a &b &c &d &e \\
f &g &h &i &j \\
k& l &m &n &o
\end{bmatrix}[/math]
```

The majority of the boards (the ones with numbers) are selectable text. Are you having trouble selecting them?

I'll print it out and meet her today.

May I ask you why she needs this?

Wait, your reasoning is correct but there are more primitive boards than you expected. 39 of them!

Here are they:

```
[[1, 7, 8, 10, 14], [11, 15, 3, 5, 6], [12, 2, 13, 9, 4]]
[[1, 7, 8, 9, 15], [10, 11, 2, 12, 5], [13, 6, 14, 3, 4]]
[[1, 7, 8, 9, 15], [11, 4, 14, 5, 6], [12, 13, 2, 10, 3]]
[[1, 7, 9, 10, 13], [8, 3, 11, 12, 6], [15, 14, 4, 2, 5]]
[[1, 7, 9, 10, 13], [8, 14, 11, 2, 5], [15, 3, 4, 12, 6]]
[[1, 6, 8, 12, 13], [9, 3, 11, 10, 7], [14, 15, 5, 2, 4]]
[[1, 6, 8, 10, 15], [11, 14, 3, 5, 7], [12, 4, 13, 9, 2]]
[[1, 6, 8, 10, 15], [11, 4, 13, 5, 7], [12, 14, 3, 9, 2]]
[[1, 6, 8, 10, 15], [9, 11, 13, 2, 5], [14, 7, 3, 12, 4]]
[[1, 6, 8, 10, 15], [9, 11, 3, 12, 5], [14, 7, 13, 2, 4]]
[[1, 6, 9, 10, 14], [8, 13, 4, 12, 3], [15, 5, 11, 2, 7]]
[[1, 5, 6, 13, 15], [11, 10, 4, 8, 7], [12, 9, 14, 3, 2]]
[[1, 5, 6, 13, 15], [11, 10, 14, 3, 2], [12, 9, 4, 8, 7]]
[[1, 5, 7, 12, 15], [9, 11, 4, 10, 6], [14, 8, 13, 2, 3]]
[[1, 5, 9, 11, 14], [8, 12, 13, 3, 4], [15, 7, 2, 10, 6]]
[[1, 5, 9, 11, 14], [10, 4, 12, 6, 8], [13, 15, 3, 7, 2]]
[[1, 5, 10, 11, 13], [9, 15, 2, 6, 8], [14, 4, 12, 7, 3]]
[[1, 5, 10, 11, 13], [9, 4, 12, 7, 8], [14, 15, 2, 6, 3]]
[[1, 4, 8, 12, 15], [10, 14, 11, 3, 2], [13, 6, 5, 9, 7]]
[[1, 4, 8, 12, 15], [10, 14, 5, 9, 2], [13, 6, 11, 3, 7]]
[[1, 4, 8, 12, 15], [9, 7, 11, 10, 3], [14, 13, 5, 2, 6]]
[[1, 4, 8, 12, 15], [9, 13, 5, 10, 3], [14, 7, 11, 2, 6]]
[[1, 4, 9, 11, 15], [10, 6, 12, 5, 7], [13, 14, 3, 8, 2]]
[[1, 4, 10, 12, 13], [8, 14, 11, 5, 2], [15, 6, 3, 7, 9]]
[[1, 3, 7, 14, 15], [10, 12, 11, 2, 5], [13, 9, 6, 8, 4]]
[[1, 3, 7, 14, 15], [10, 12, 6, 8, 4], [13, 9, 11, 2, 5]]
[[1, 3, 8, 13, 15], [9, 11, 12, 6, 2], [14, 10, 4, 5, 7]]
[[1, 3, 9, 13, 14], [11, 15, 5, 7, 2], [12, 6, 10, 4, 8]]
[[1, 3, 10, 11, 15], [9, 8, 12, 6, 5], [14, 13, 2, 7, 4]]
[[1, 3, 10, 11, 15], [9, 8, 12, 7, 4], [14, 13, 2, 6, 5]]
[[1, 3, 11, 12, 13], [8, 7, 9, 10, 6], [15, 14, 4, 2, 5]]
[[1, 3, 11, 12, 13], [9, 6, 8, 10, 7], [14, 15, 5, 2, 4]]
[[1, 2, 9, 13, 15], [11, 14, 5, 4, 6], [12, 8, 10, 7, 3]]
[[1, 2, 9, 13, 15], [11, 14, 5, 7, 3], [12, 8, 10, 4, 6]]
[[1, 2, 10, 13, 14], [11, 15, 5, 3, 6], [12, 7, 9, 8, 4]]
[[1, 2, 11, 12, 14], [8, 9, 10, 7, 6], [15, 13, 3, 5, 4]]
[[1, 2, 11, 12, 14], [8, 13, 10, 5, 4], [15, 9, 3, 7, 6]]
[[1, 2, 11, 12, 14], [10, 7, 8, 9, 6], [13, 15, 5, 3, 4]]
[[1, 2, 11, 12, 14], [10, 15, 8, 3, 4], [13, 7, 5, 9, 6]]
```

[[a, b, c, d, e], [f, g, h, i, j], [k, l, m, n, o]] represents the following matrix:

So, the rest of your reasoning is okay since 39 * 5! * 3! = 28080

Oh okay.

I just wrote some code and I am getting 28080. I might have done something wrong but I will postpone checking my code till tomorrow.

Maybe our beloved bobbym can help.

I believe your conclusion about permuting the "basic" board is correct.

But are you doing all of these by hand?

**Agnishom**- Replies: 41

If

Find

The answer should have a closed form like

Should I place one integers from 1 to 15 exactly once in the board?

This is an interesting question, nevertheless.

Where is this problem from?

with mathematical proof

You are going to have trouble defining what a mathematical proof is.

Okay, have fun.

Why is becoming julianthemath a bad thing?

No but I am sure you meant something else.