Math Is Fun Forum
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#51 2013-12-30 13:04:43
Re: Simple Combinatorics Problem
It is still confusing and different from the other two problems
'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'
I'm not crazy, my mother had me tested.
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#52 2013-12-30 16:59:01
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Yes, it is. Generating functions mostly look the same. Every once in a while you have to be a little creative.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#53 2013-12-30 17:17:37
Re: Simple Combinatorics Problem
Okay; What now?
'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'
I'm not crazy, my mother had me tested.
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#54 2013-12-30 17:30:47
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
What are your coin denominations?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#55 2013-12-30 17:43:14
Re: Simple Combinatorics Problem
0.1, 0.25, 0.5, 1, 2, 5, 10
How many ordered pair of integers (x,y) are there such that 1 <= x <= 10 and 1 <= y <= 10 and (x-5)(y-5) = 0?
Is it possible to do it with gfs?
'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'
I'm not crazy, my mother had me tested.
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#56 2013-12-30 17:50:21
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
The answer is 19.
Do not use a cannon to kill a mosquito.
What are they called, those monetary denominations?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#57 2013-12-30 18:01:23
Re: Simple Combinatorics Problem
What can they be called for example?
I know that the answer is 19 but I do not see how you can use a gf on 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'
I'm not crazy, my mother had me tested.
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#58 2013-12-30 18:05:16
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Offhand I do not see how either. But the solution is so simple it is not necessary.
Supposing I wanted to make change for 100 whatever from those coins which I have in unlimited supply. How many ways can I do this?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#59 2013-12-30 18:13:24
Re: Simple Combinatorics Problem
Sounds like a partitioning problem
'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'
I'm not crazy, my mother had me tested.
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#60 2013-12-30 18:17:44
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Exacta Mundo! The favorite type of Ramanujan and Hardy.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#61 2013-12-30 18:18:50
Re: Simple Combinatorics Problem
because 1000 is the maximum number of coins you'll need
Last edited by Agnishom (2013-12-30 18:19:22)
'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'
I'm not crazy, my mother had me tested.
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#62 2013-12-30 18:20:03
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
That is not correct but do not worry, you have to see these to get good at them.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#63 2013-12-30 18:30:00
Re: Simple Combinatorics Problem
Oh sorry, there is a 1+
'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'
I'm not crazy, my mother had me tested.
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#64 2013-12-30 18:34:43
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Want to see how to do it?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#65 2013-12-30 18:35:52
Re: Simple Combinatorics Problem
Indeed but is the above correct?
'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'
I'm not crazy, my mother had me tested.
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#66 2013-12-30 18:38:28
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
That is not correct.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#67 2013-12-30 18:39:15
Re: Simple Combinatorics Problem
What is the correct function then?
'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'
I'm not crazy, my mother had me tested.
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#68 2013-12-30 18:42:08
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
First, we like to deal with integers in the exponents so multiply everything by 100.
{0.1, 0.25, 0.5, 1, 2, 5, 10, 100}*100 = {10., 25., 50., 100, 200, 500, 1000, 10000}
Have to get off for a while. Delivery to check.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#69 2013-12-30 18:52:26
Re: Simple Combinatorics Problem
Why would you do that?
delivery to check
What is that?
Last edited by Agnishom (2013-12-30 18:55:07)
'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'
I'm not crazy, my mother had me tested.
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#70 2013-12-30 21:45:30
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Simple Combinatorics Problem
The main trick (technique?) I use is to see it as a linear diophantine equation. I'm not aware of any g.f like solutions for non-linear ones, because addition of terms in linear equations is equivalent to multiplication of polynomials in g.f.
The partitioning problem can be written as
'a' consists of multiples of 10, 'b' of 25's, 'c' of 50's ...
So, the g.f can be written as
or, in short,
and you need [x^n] for the number of ways.
For the problem in the first post, indicate it by the equation
x_1 is the youngest and x_10 is the oldest aspirant. Indicate them by a different variable.
Write the g.f
This indicates a boolean, the aspirants are selected or not.
Now collect the coefficients of terms where x and y powers add up to 5, but not the one having y^2.
"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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#71 2013-12-30 22:36:02
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Why would you do that?
Technically, from maxima's point of view it would not matter but when we are dealing with polynomials they have integer exponents.
gAr has illustrated the whole idea I was getting at. How much do you understand and where are you stuck?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#72 2013-12-30 23:41:48
Re: Simple Combinatorics Problem
I am stuck at the line which begins with G(x)
'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'
I'm not crazy, my mother had me tested.
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#73 2013-12-30 23:53:58
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Simple Combinatorics Problem
We are using
"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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#74 2013-12-30 23:59:30
Re: Simple Combinatorics Problem
Is it one of the formulas for geometric progression?
'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'
I'm not crazy, my mother had me tested.
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#75 2013-12-31 00:24:48
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Simple Combinatorics Problem
That's right.
"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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