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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,264

What part of the question? a, b?

**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: 15,522

a, for starters.

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: 86,264

Know how to simulate or enumerate it?

**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: 15,522

I would try a simulation, but I'm on my phone. I do not have access to a CAS.

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: 86,264

What do you want me to do then?

**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: 15,522

I was just asking if you've seen it and if you have any ideas for 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: 86,264

I have not looked at it but first I would run a simulation. As soon as I write it of course.

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: 15,522

Hm, what name did he use for you in that pdf?

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: 86,264

That is the name he took from the email I sent him!

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: 15,522

How many email accounts do you have?

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: 86,264

2 for everyday use. 1 for sites that I do not trust.

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: 15,522

Which one do you email me from? The last one?

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: 86,264

One of them has no storage capability so I have clean out the spam frequently. I use the Lycos for you.

Simulation checks out his answer.

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: 15,522

bobbym wrote:

Know how to simulate or enumerate it?

How do I simulate 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: 86,264

That quote was written over a thousand years ago, please refresh my memory.

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: 15,522

Drop dead, the game from the dice PDF. How do I simulate 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: 86,264

```
s=0;
fubar[L_]:=Module[{s=0,ans=L},
While[ans!={},
ans = RandomChoice[{1,2,3,4,5,6},Length[ans]];
If[Count[ans,2|5]==0,s+=Total[ans],ans=DeleteCases[ans,2|5]];
];
s]
Table[fubar[ RandomChoice[{1,2,3,4,5,6},5]],{100000}]//Mean//N
```

16.08264

All indentations for readability taken out.

This is a really poor effort and you should avoid programming in this manner.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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

Hi,

Using the technique from http://mathisfunforum.com/viewtopic.php … 63#p265663, we can utilize a table instead, since recursion in this case is prohibitive.

```
k = 3 # a face appears k times
n = 10
throws = [[[[[[0]*n for _ in xrange(n)] for _ in xrange(n)] for _ in xrange(n)] for _ in xrange(n)] for _ in xrange(n)] # a 6-dimensional list
for a in range(k+1):
for b in range(k+1):
for c in range(k+1):
for d in range(k+1):
for e in range(k+1):
for f in range(k+1):
if (a == 0 or b == 0 or c == 0 or d == 0 or e == 0 or f == 0):
throws[a][b][c][d][e][f] = 6*k - (a+b+c+d+e+f)
else:
throws[a][b][c][d][e][f] = float(throws[a-1][b][c][d][e][f]+throws[a][b-1][c][d][e][f]+throws[a][b][c-1][d][e][f]+throws[a][b][c][d-1][e][f]+throws[a][b][c][d][e-1][f]+throws[a][b][c][d][e][f-1])/6
print throws[k][k][k][k][k][k]
```

Perhaps we can solve more problems involving trees this way.

"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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