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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

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.

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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: 88,998

You mean labeling the vertices with the sums?

**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
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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: 88,998

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

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: 88,998

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

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.

**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
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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.

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

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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!

**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
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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!

**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: 15,606

Then what?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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There is an interesting little idea in Computer math that might help.

**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: 15,606

Diagonalization?

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

**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: 15,606

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?

**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: 15,606

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
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Then that is proof of ESP.

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

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

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