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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

Oh.

```
list = {300, 250, 175, 100, 75, 50, 25, 15, 7, 3, 1}
SecondPick[tickets_] := Sum[i/1001*tickets/(1001 - i), {i, Delete[list, Position[list, tickets]]}];
```

*Last edited by anonimnystefy (2013-05-02 07:11:41)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Code, code, give me code! Okay, thank you.

Code, code, a thousand lines of code. I'd rather die then debug it. Sung to the tune of "No, no, a thousand times no. I'd rather die then say yes."

**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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I am not sure what you want.

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: 86,161

Nothing, just singing an old song with my improved lyrics.

**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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Have you looked at the code?

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: 86,161

I just copied it to my notebook that deals with this problem.

I must warn you that I am missing a couple of great abilities that God in his infinite wisdom decided not to bestow on me.

**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: 15,518

What are those abilities?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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The list appears endless but the one that applies is that I never could read code written by someone else.

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: 15,518

Give me a few minutes to eat. When I get back, I will explain it a bit.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Very good, I will eat and continue to explore mythological creatures from Serbia.

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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Mythological creatures? Like which?

To be honest, I never took much interest into Slavic mythology.

Now, for the code...

I am just summing P(second pick by n|first pick by i).

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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I see that. But my general approach to computing the exact numbers here would be to tree it.

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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Tree it? How?

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**bobbym****Administrator**- From: Bumpkinland
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You aware that Markov chains and gf's can be compact representations of trees?

There is just one tiny little, itsy bitsy problem...

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 do not know how useful Markov chains are here. The probabilities change for different previous picks.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Exact a mundo! GF's will have the same problem. But if you had a big piece of paper you could do it...

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 do not think it will be enough for picks higher than the second.

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**bobbym****Administrator**- From: Bumpkinland
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Nope, if I had a big piece of paper, I could just enumerate the entire tree. From beginning to end.

What I am getting at is how to do this using M and whatever structure is available. How to draw it without drawing. Now it is obvious we could use 11 nested loops but we should strive to use something a bit more elegant than that.

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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Well, Markov chains require the probabilities to stay the same, but maybe we can do something with GF's?

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**bobbym****Administrator**- From: Bumpkinland
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First, I am trying to work out the answer using programming.

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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That will be hard.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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For instance:

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: 15,518

How'd you get those?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Wrote a little program to do it for me.

As you can see all answers are close to my simulation.

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: 15,518

Can you post the program code?

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