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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,743

By writing a program in M and running it.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

I know that. But, did you fill the square and then check all differences or did you do it by filling the squares one by one?

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: 88,743

I could write down the pseudocode for the algorithm.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Sure! Just hide it!

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: 88,743

Hi;

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Have you finished writing the pseudo-code yet?

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: 88,743

Hi;

Not yet, I got busy with something else.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Okay.

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: 88,743

Hi;

Pseudocode provided.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Hi bobbym

Have you actually tried running the code, because I don't thnk it would work...

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: 88,743

Hi;

It probably would not work. The pseudocode monster came and ate it up.

**In mathematics, you don't understand things. You just get used to them.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

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?

Got 433 for the 3x3 matrix, so I'm hopeful that it's the answer.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,743

Hi gAr;

That is what we got too! I never did get an answer for a 5 x 5 and an 11 x 11, yikes!

**In mathematics, you don't understand things. You just get used to them.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Last month, I worked out a generating function with 3 variables for 3x3, can't find the sheet where I worked it out!

Anyway, there was no symmetry or pattern in it, and 5x5 would need 5 variables and much more complicated.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,743

Hi;

I sure would have liked to have seen that gf for the 3 x 3. I tried a recurrence or two but nothing seemed to work.

**In mathematics, you don't understand things. You just get used to them.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

I'm working on gf for 3x3 again, may take some time.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Hi gAr

If you have three variables, each one must stand for something. What would [x[sup]n[/sup]]F(x,y,z), [y[sup]n[/sup]]F(x,y,z) and [z[sup]n[/sup]]F(x,y,z) represent?

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

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Sorry, it's 2 variables for 3x3

*Last edited by gAr (2013-01-08 06:27:17)*

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,743

Hi gAr;

It sure does get the right answer!

**In mathematics, you don't understand things. You just get used to them.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Yes! In the same manner, we can use 4 variables for 5x5 matrix, but requires too many cases to consider, quite a problem!

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,743

Hi;

I have had the same problem with every approach, too complicated to go to the 5 x 5.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

I think this is the hardest question I ever posed, besides "Why?".

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: 88,743

It is very valuable to you, is it not?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

What is?

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: 88,743

You may learn the Colonel's dictum.

**In mathematics, you don't understand things. You just get used to them.**

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