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## #26 2013-09-22 03:45:29

bobbym

Online

### 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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #27 2013-09-22 03:48:26

anonimnystefy
Real Member

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### Re: Combinatorics

But, there aren't 4 types of pens.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #28 2013-09-22 03:50:52

bobbym

Online

### 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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #29 2013-09-22 03:53:05

anonimnystefy
Real Member

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### 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.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #30 2013-09-22 03:54:50

anonimnystefy
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### Re: Combinatorics

Here is a code that gets the correct answer

#### Code:

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 (2013-09-22 03:55:02)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #31 2013-09-22 03:58:46

bobbym

Online

### Re: Combinatorics

Okay, let me try that.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #32 2013-09-22 03:59:35

anonimnystefy
Real Member

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### Re: Combinatorics

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #33 2013-09-22 04:01:50

bobbym

Online

### 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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #34 2013-09-22 04:05:08

anonimnystefy
Real Member

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### Re: Combinatorics

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #35 2013-09-22 04:07:13

bobbym

Online

### Re: Combinatorics

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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #36 2013-09-22 04:08:51

anonimnystefy
Real Member

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### Re: Combinatorics

Those numbers are used just for differentiating the pens.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #37 2013-09-22 04:14:53

bobbym

Online

### 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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #38 2013-09-22 04:17:04

anonimnystefy
Real Member

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### 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.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #39 2013-09-22 04:19:38

bobbym

Online

### 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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #40 2013-09-22 09:45:42

bob bundy
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### 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

## #41 2013-09-22 09:47:37

anonimnystefy
Real Member

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### Re: Combinatorics

144?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #42 2013-09-22 09:52:04

bob bundy
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### 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

## #43 2013-09-22 10:00:01

anonimnystefy
Real Member

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### Re: Combinatorics

Ah, okay.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #44 2013-09-22 12:32:21

bob bundy
Moderator

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### Re: Combinatorics

Here they are:

Bob

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

## #45 2013-09-22 13:14:35

Agnishom
Real Member

Online

### 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'
'The whole person changes, why can't a habit?' -Alokananda

## #46 2013-09-22 18:51:35

bobbym

Online

### 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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #47 2013-09-22 20:55:15

Agnishom
Real Member

Online

### 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'
'The whole person changes, why can't a habit?' -Alokananda

## #48 2013-09-22 20:59:02

bobbym

Online

### Re: Combinatorics

http://maths.freeforums.org/

Did you expand his gf?

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

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #49 2013-09-23 00:07:01

Agnishom
Real Member

Online

### Re: Combinatorics

'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'
'The whole person changes, why can't a habit?' -Alokananda

## #50 2013-09-23 00:16:43

anonimnystefy
Real Member

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### Re: Combinatorics

Hi Agnishom

You can also check out this thread: http://www.mathisfunforum.com/viewtopic … 04&p=2.  Bobbym gave some interesting examples in that thread which use GFs like I did for the problem in this thread.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment