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#26 2013-09-21 05:45:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,124

Re: Combinatorics

That makes sure there are 4 different types and removes duplicates.


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

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#27 2013-09-21 05:48:26

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,609

Re: Combinatorics

But, there aren't 4 types of pens.


“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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#28 2013-09-21 05:50:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,124

Re: Combinatorics

Yes there is, type 1,2,3, and 4. They are the second number in each list.


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

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#29 2013-09-21 05:53:05

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,609

Re: Combinatorics

Nowhere in the problem is stated that we can't choose both red1 and green1. That is the main problem with the definition of ans2.


“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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#30 2013-09-21 05:54:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,609

Re: Combinatorics

Here is a code that gets the correct answer

s = {{r, 1}, {r, 2}, {b, 1}, {b, 2}, {b, 3}, {g, 1}, {g, 2}, {g, 3}, {g, 4}};
ans = Permutations[s, {4}];
ans1 = Select[ans, Length[Union[#[[All, 1]]]] == 3 &];
ans2 = Union[Sort /@ ans1] // Length

Last edited by anonimnystefy (2013-09-21 05:55:02)


“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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#31 2013-09-21 05:58:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,124

Re: Combinatorics

Okay, let me try that.


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

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#32 2013-09-21 05:59:35

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,609

Re: Combinatorics

I have noticed it is pretty much the same as yours except it doesn't have the ans2 line.


“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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#33 2013-09-21 06:01:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,124

Re: Combinatorics

How does it deal with this part?

You want to purchase 4 pens, each of a different type

Where is that condition done?


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

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#34 2013-09-21 06:05:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,609

Re: Combinatorics

It's the ans1 line, which is the same as yours.


“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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#35 2013-09-21 06:07:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,124

Re: Combinatorics

The first correct answer is

But if the second numbers are the types, this one only has 2 different types, not 4.


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

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#36 2013-09-21 06:08:51

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,609

Re: Combinatorics

Those numbers are used just for differentiating the pens.


“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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#37 2013-09-21 06:14:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,124

Re: Combinatorics

I think you are correct but I do not agree with the problem wording. It is my major dislike of that site.


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

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#38 2013-09-21 06:17:04

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,609

Re: Combinatorics

If the problem with this problem's wording is that it says type, you should know type refers to the colour.

What the problem with that site is, is most of the problems are user submitted and probably not very much checked.


“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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#39 2013-09-21 06:19:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,124

Re: Combinatorics

That is where I did not get that idea and came up with a different answer.
Luckily this was not in my problem set.


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

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#40 2013-09-21 11:45:42

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,471

Re: Combinatorics

I have a complete list.  I used my method of post 2, eliminating repeats.  There are 72.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#41 2013-09-21 11:47:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,609

Re: Combinatorics

144?


“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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#42 2013-09-21 11:52:04

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,471

Re: Combinatorics

No 72.  I just re-read the question and took out the repeated types.

It's just 24 x 6 divided by 2.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#43 2013-09-21 12:00:01

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,609

Re: Combinatorics

Ah, okay.


“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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#44 2013-09-21 14:32:21

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,471

Re: Combinatorics

Here they are:

Bob

View Image: pens.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#45 2013-09-21 15:14:35

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,205
Website

Re: Combinatorics

I don't really understand how GFs are used. Could anyone teach me?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#46 2013-09-21 20:51:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,124

Re: Combinatorics

You asked that question in the other forum that we are both members of. I believe it was about partitions.

Generating functions are a way to change a combinatorics problem into a computational one. What would you like to do with them?


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

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#47 2013-09-21 22:55:15

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,205
Website

Re: Combinatorics

this problem.

stefy's forum? I've lost the link


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#48 2013-09-21 22:59:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,124

Re: Combinatorics

http://maths.freeforums.org/

Did you expand his gf?

We also had a good discussion about gf's right here.

http://www.mathisfunforum.com/viewtopic … 87#p268687


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

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#49 2013-09-22 02:07:01

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,205
Website

Re: Combinatorics

We had, but I'm not confident about it


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#50 2013-09-22 02:16:43

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,609

Re: Combinatorics

Hi Agnishom

You can also check out this thread: http://www.mathisfunforum.com/viewtopic … =17704&p=2.  Bobbym gave some interesting examples in that thread which use GFs like I did for the problem in this thread.


“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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