Math Is Fun Forum
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#76 2013-12-31 00:32:15
Re: Simple Combinatorics Problem
So, how many ways are there to get Rs 100? How do I compute the answer?
'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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#77 2013-12-31 00:34:21
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Simple Combinatorics Problem
You have to find the coefficient of x^10000.
"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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#78 2013-12-31 00:43:44
Re: Simple Combinatorics Problem
Why is the expansion function not working properly?
(%i4) expand((1/((1-x^10)*(1 - x^25)*(1-x^50)*(1-x^100)*(1-x^200)*(1-x^500)*(1-x^1000))));
1885 1875 1860 1850 1835 1825 1810 1800
(%o4) 1/(- x + x + x - x + x - x - x + x
1785 1775 1760 1750 1735 1725 1710 1700 1685
+ x - x - x + x - x + x + x - x + x
1675 1660 1650 1635 1625 1610 1600 1585 1575
- x - x + x - x + x + x - x - x + x
1560 1550 1535 1525 1510 1500 1385 1375 1360
+ x - x + x - x - x + x + x - x - x
1350 1335 1325 1310 1300 1285 1275 1260 1250
+ x - x + x + x - x - x + x + x - x
1235 1225 1210 1200 1185 1175 1160 1150 1135
+ x - x - x + x - x + x + x - x + x
1125 1110 1100 1085 1075 1060 1050 1035 1025
- x - x + x + x - x - x + x - x + x
1010 1000 885 875 860 850 835 825 810 800 785
+ x - x + x - x - x + x - x + x + x - x - x
775 760 750 735 725 710 700 685 675 660 650
+ x + x - x + x - x - x + x - x + x + x - x
635 625 610 600 585 575 560 550 535 525 510
+ x - x - x + x + x - x - x + x - x + x + x
500 385 375 360 350 335 325 310 300 285 275
- x - x + x + x - x + x - x - x + x + x - x
260 250 235 225 210 200 185 175 160 150 135
- x + x - x + x + x - x + x - x - x + x - x
125 110 100 85 75 60 50 35 25 10
+ x + x - x - x + x + x - x + x - x - x + 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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#79 2013-12-31 00:49:50
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Simple Combinatorics Problem
When there are variables in denominator, you need to use taylor expansion
Try
coeff(taylor(1/((1-x^10)*(1-x^25)*(1-x^50)*(1-x^100)*(1-x^200)*(1-x^500)*(1-x^1000)),x,0,10000),x,10000)= 95772831
"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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#80 2013-12-31 00:55:16
Re: Simple Combinatorics Problem
Oh Wow! Thanks 
'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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#81 2013-12-31 01:03:12
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Simple Combinatorics Problem
You're welcome!
"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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#82 2013-12-31 05:03:44
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
95772831 is 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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#83 2013-12-31 05:51:30
Re: Simple Combinatorics Problem
How can you say for sure?
'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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#84 2013-12-31 05:57:48
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
If you want truth then you have to study philosophy. If you want certainty, you study religion. In computational math we have neither but that does not stop us from being able to build computers, flt craft, particle beams, ag reactors using it.
There is a good rule that provides us with some confidence in the result.
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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#85 2013-12-31 06:04:56
Re: Simple Combinatorics Problem
And what is that rule?
'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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#86 2013-12-31 06:06:16
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Have you been following the thread in Computer math about getting the coefficient?
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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#87 2013-12-31 06:13:30
Re: Simple Combinatorics Problem
No
'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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#88 2013-12-31 06:19:25
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
That is too bad because the question is answered there.
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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#89 2013-12-31 06:36:39
Re: Simple Combinatorics Problem
The answer is 42. The question is the 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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#90 2013-12-31 06:47:05
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Let me ask you a question. When you ask your calculator √45 and it spits out 6.708203932499369 how do you know that is right. Why do you trust it? When you go to the store and the guy rings up 1127.45 with his machine do you question it?
Yes, how do you know anything for certain?
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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#91 2013-12-31 06:53:39
Re: Simple Combinatorics Problem
6.708203932499369
You can multiply by hand and see that the answer is close to 45.
what is that 1127.45 mean?
'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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#92 2013-12-31 06:56:04
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
How about when I tell you the millionth digit of pi is a 5? Can you check that by hand? Do you really check every square root by multiplication? Who checks your multiplication?
what is that 1127.45 mean?
That is your bill for something.
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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#93 2013-12-31 06:58:48
Re: Simple Combinatorics Problem
I do not check that always. In some way I am vulnerable to the machine in case it chooses to betray me.
If the bill is not okay, I'll go to the consumer court
'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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#94 2013-12-31 07:05:07
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
And what court do you go to for the millionth digit of pi?
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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#95 2013-12-31 07:09:36
Re: Simple Combinatorics Problem
I do not know. I'll report you to the administrator if I find out you're wrong.
'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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#96 2013-12-31 07:16:05
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
They used the method I mentioned to gain confidence in every pi calculation done.
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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#97 2013-12-31 07:20:32
Re: Simple Combinatorics Problem
WWho are they? What method? Confidence for what?
'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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#98 2013-12-31 07:26:29
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Have you not thought how they verify to their peers what the trillionth digit of pi is? Do you think you can just say it is a 4 and write a paper and get another research grant?
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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#99 2013-12-31 12:59:47
Re: Simple Combinatorics Problem
Ofcourse not. They have to explain how they determined 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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#100 2013-12-31 13:40:13
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
That is not good enough for numerical work. Supposing the algorithm is flawed or the program implementing it has a bug. This is your question, how can we be sure?
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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