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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

bobbym wrote:

There is another more general way. That maybe can answer for many missing intersections.

I like your first method. It is easily programmable.

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: 87,237

You mean labeling the vertices with the sums?

**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
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Yep. DP is really nice.

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: 87,237

But there is a much nicer way that is probably quicker too!

**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: 15,544

Which is?

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: 87,237

I am being called away so I will show the method as soon as I get back.

**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: 15,544

Okay, no hurry. And if they threaten you, just ask yourself WWHD?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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WWHD? Why Would Hay Decompose?

Now run

MatrixPower[A, 8][[1]]

the last entry means from 1 to 24, 38 ways.

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: 15,544

It takes much londer if you have a larger grid. I'd say DP is better here.

WWHD - What Would Hulk Do?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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The matrix can be filled by a program as the "Dice" guy does. Also it is a lot easier for a computer to do.

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
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I'm not sure if getting the 8th piwer if a huge matrix is fast.

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
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Hohohohohohohoo! That is a good one! I just talked to Mathematica and he said it sure is. Also there are ways to just get one element of that matrix!

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
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What if you had a grid 100 by 100. You would need to get th 100th power of a 10201 by 10201 matrix!

*Last edited by anonimnystefy (2013-10-15 04:33:59)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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You would not!

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: 15,544

Then what?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,237

There is an interesting little idea in Computer math that might help.

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: 15,544

Diagonalization?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Matrix moves is the one.

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: 15,544

I'd say that's the same thing I said.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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About what?

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: 15,544

I meant to say that I think me were thinking about the sane thing in posts #42 and #43.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,237

Then that is proof of ESP.

Were you also thinking about a big corned beef sandwich? No? Neither was I! Another amazing coincidence or...

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

Combinatorics is Algebra and Algebra is Combinatorics.

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