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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Okay, no problem. I will come up with something.

**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: 15,525

Okay, thanks.

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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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 291

I would like to see a new problem too

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

I am posting it now.

**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: 3,848

Hi Bobby and stefy,

bobbym wrote:

Are you attempting to solve this with a simulation?

Yes...as per the question. I hadn't even considered the much sounder and accurate mathematical alternative and the craziness of such a large sim!

Thanks for the fix for my B version, Bobby...took me a while to understand it, but I finally got it.

I tried the codes that both of you posted, but I particularly like this sim one of stefy's as it's brief, fast and I can understand it:

anonimnystefy wrote:

Here is my own code with no strings:

`Count[Table[RandomInteger[], {10000}, {10}], {___, 1, 1, 1, 1, ___}]/10000 // N`

I didn't know that pattern trick, so that was nice to learn.

This slightly amended code reduces processing time by about 40%:

`Count[Table[RandomInteger[1, 10], {10000}], {___, 1, 1, 1, 1, ___}]/10000 // N`

That blindingly-fast code in post #58 erred if I'd used 'a' or 'n' elsewhere in the current M run, but "ClearAll["Global`*"];" at the beginning fixed that. Found it on the net.

*Last edited by phrontister (2013-05-03 06:03:11)*

"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: 86,676

Hi;

The important part is the Tuples command, if you understand that...

**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: 3,848

Oops! Yes, I was amazed at the speed and short code, but before understanding it properly I started reading all the other posts that followed and clean forgot to get back to it. I did look up Tuples and Cases at the time and think I'm nearly there with it, but I'll have a closer look after I've been to bed...which is where I should have been hours ago!

So many ways to skin a cat!

"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: 86,676

M has that feature. It is nice but it is confusing. See you later.

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: 15,525

bobbym wrote:

I am posting it now.

Thanks!

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: 86,676

I posted it a long time ago.

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: 15,525

I know. But, I haven't had a chance to post when you posted 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: 86,676

That is okay. Good luck with the problem and may the M be with you.

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: 15,525

Well, I'll leave this one until he sees and reads 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: 86,676

He might start working on it himself.

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: 15,525

He probably will. I just do not want him to abandon it because a discussion of it has started.

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: 86,676

Well, I hope the comments of A and C and especially D do not lead him astray.

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: 15,525

Me too.

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: 86,676

Okay, I have to go shopping so I will see you later.

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: 15,525

Okay, see you.

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: 86,676

Where am I going? Bought some food and I am eating it.

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: 3,848

Hi Bobby,

bobbym wrote:

...and may the M be with you.

And May the Fourth be with you!

Yes...that Tuples command is interesting, generating all those possibles like that. Length was new to me too, and I didn't know about the use of "//" either. So...thanks for introducing them.

Early to bed for a change. Catch you later.

"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: 86,676

The Fourth?

Have a good night.

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: 3,848

bobbym wrote:

The Fourth?

Either that's today's date, or I've developed a bad spelling lithp.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

I thought it was the fifth over there.

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: 3,848

It is now, but not when I wrote that last night. I'd waited with that post until it was the fourth both in Oz and the U.S.

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