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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

I am not able to draw any generalized conclusions, but I think I sorta get the point.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Then you are not getting the point yet.

2 Corinthians 6:17 wrote:

Go out from amongst them and be ye separate.

Same point! But what does it mean when we are talking about problem solving in mathematics.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

Learn new tehniques for solving problems?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Nope, learning different ones from what everyone is taught and learns. Back engineering from solution to method to question is one tool. We do not work front to back as they do. We work back to middle, front to middle, middle to front, any way that solves the problem.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

Hi Bobby,

M's 'RootReduce' on 1/Sqrt[1600 - x^2] + 1/Sqrt[2500 - x^2] == 1/10 gives the polynomial

x^8 - 7800 x^6 + 22350000 x^4 - 27838000000 x^2 + 12728100000000 = 0.

'N(Solve' on both equations gives

A. 37.355085334132530453574972651850703481315230858701, but the polynomial has an additional root:

B. 39.279615487303641329301362495489316846168383844149

Loading A & B back into the polynomial gives the following:

A. -3.303*10^-50

B. 9.0*10^-52

They're much closer to each other than when loading A & B back into the fraction equation, which gives these results:

A. 0.10000000000000000000000000000000000000000000000000000000000003843105

B. 0.16464704210781912709568407854860421540174931326784531936682258297947

In the words of Julius Sumner Miller: "Why is it so?"

Also, why can't I get W|A to give me the polynomial with RootReduce[Solve[1/Sqrt[1600 - x^2] + 1/Sqrt[2500 - x^2] == 1/10, x]]? It ignores the RootReduce function and instead displays a graph, three alternate forms of the original equation, and the root (positive and negative).

Don't worry about spending too much time sorting this out for me if the answer isn't simple enough for me to understand (you know what I mean).

*Last edited by phrontister (2012-11-05 18:46:17)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Hi phrontister;

Sometimes algebraic manipulations of the kind you did introduce spurious roots.

Alpha is not the complete Mathematica package. It behaves differently.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

Thanks, Bobby. I'll leave that there then.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Hi phrontister;

No problem keep on experimenting with your ideas!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

**New problem:**

**WDYT #200:**

**Inspired by the other thread C creates another similar problem.**

**What is the area of the circle that has two perpendicular chords with lengths as shown in the diagram.**

**A says) A great problem C. I have the answer!**

**B says) Bah humbug!**

**C says) Why the negative attitude B? Is my problem too tough for ya?**

**D says) Yes, B is a math wimp. I solved it!**

**E says) Double humbug, B is right. Those solutions are kaboobly doo.**

**A says) Why!**

**E says) Maybe because...**

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

Hi

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

Hi

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

Hi

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

Yes, I have. And I solved it.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Hi;

I does look like you have done it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

Hi bobbym

I hope you don't mind me posting this. If you do, feel free to remove this post.

**Here's a new problem:**

**You have a square of side 5 divided into 25 unit squares. In the central square a 0 is placed.Question: In how many ways can the square be filled with non-negative numbers so that the absolute difference of numbers in two adjacent squares is never greater than 1? What is the answer if the large square has a side of 11 instead?**

*Last edited by anonimnystefy (2012-12-09 05:37:08)*

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Hi anonimnystefy;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

Let me guess, that was a wild guess to see if I have the answer yet or not.

I a now wondering why I posted it without having the solution...

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

That is not a wild guess but what I think is the answer unless my arithmetic is bad.

Some people hate broccoli, some people hate liberals, most people hate bobbym, everyone hates math, I hate hand calculations!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

It's not true that everybody hates math!

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Maybe but they all hate broccoli and bobbym.

What do you think of my solution and do you require the 11 x 11?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

Not everyone hates bobbym, either!

I am still unable to verify your answer. Sorry.

Maybe I should delete the problem and post it when I have the answer...

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Hi;

You could leave it. Where does the problem come from?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**