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#726 2011-07-01 21:57:37

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Is this cool with you?

Hi,

Here's a python script.

cnt = 0
cnt10 = 0
for a in (1,2,4,8,16):
    for b in (1,2,4,8,16):
        for c in (1,2,4,8,16):
            for d in (1,2,4,8,16):
                for e in (1,2,4,8,16):
                    if a<=b and b<=c and c<=d and d<=e:
                        cnt += 1
                        print a,b,c,d,e
                        if a+b+c+d+e == 10:
                            cnt10 += 1
print cnt,cnt10

Correct, isn't it?


"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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#727 2011-07-01 22:07:45

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Is this cool with you?

Hi gAr;

I believe so. I am now getting 126 also. I do not where the error came from. That clears up one problem, thanks!


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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#728 2011-07-01 22:13:39

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

Okay, nice to hear that!
Is 126 the answer then?


"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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#729 2011-07-01 22:18:59

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Is this cool with you?

Yes! Also there seems to be a simple combinatorial answer!


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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#730 2011-07-01 22:29:33

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Is this cool with you?

Cool!

there seems to be a simple combinatorial answer!

Number of terms in the expansion of (a+b+c+d+e)^5 ?

But I'm still a little confused.
Instead, if B had got (2,2,2,2,2) twice or (4,2,2,1,1) twice, will it still be the same answer?
Are the events of getting (2,2,2,2,2) and getting (4,2,2,1,1) equiprobable?


"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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#731 2011-07-01 22:38:02

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Is this cool with you?

Hi;

Those are equiprobable. Each of the 5 areas that he can hit all are equiprobable. Each one has a point value associated with it. So with one dart scoring 2 is just as likely as scoring 1. So with 5 darts 1,1,1,1,1 is as likely as 2,2,2,2,2 or 4,2,2,1,1.


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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#732 2011-07-01 22:46:53

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Is this cool with you?

Hi,

Okay, thanks.

If B had got only one game with a score of 10 (say 2,2,2,2,2), can we still estimate the number of games?


"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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#733 2011-07-01 22:58:22

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Is this cool with you?

Hi gAr;

The equiprobable aspect of the question was only brought in to state that there was no bias. The problem could have phrased in a way that removed any mention of a probability but I wanted to save that for later. When I knew a little more.

Anyways the number of games is:

As long as areas to hit equals darts. In this case.


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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#734 2011-07-01 23:17:37

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

Okay. Thanks for the formula!
So they are the number of coefficients in the expansion of multinomial, like I doubted in #732.


"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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#735 2011-07-01 23:58:15

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Is this cool with you?

Hi gAr;

I am not following you there. The largest coefficient is 120 in that expansion. I am not sure how to get 126 out of 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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#736 2011-07-02 00:04:20

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Is this cool with you?

Hi,

I meant this: http://en.wikipedia.org/wiki/Multinomia … efficients

In our case:
m=5, n=5


"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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#737 2011-07-02 00:09:30

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Is this cool with you?

Hi gAr;

It will not work for 6 darts and 6 areas.


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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#738 2011-07-02 00:18:23

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Is this cool with you?

Hi,

I got it correct.


"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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#739 2011-07-02 00:26:40

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Is this cool with you?

Hi gAr;

I am getting


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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#740 2011-07-02 00:32:20

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

You didn't include the 6th point value, did you??


"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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#741 2011-07-02 00:34:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Is this cool with you?

I used the same areas but just 6 darts. That is no good?


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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#742 2011-07-02 00:42:48

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Is this cool with you?

You told it wouldn't work for 6 darts and 6 areas.
Did you mean 6 darts and 5 areas?
For that I'm getting same as yours.

n is the number of darts
m is the number of areas.
Did you also assume the same 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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#743 2011-07-02 00:44:58

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Is this cool with you?

Hi gAr;

The confusion is because the problem is stated in a way that is the same but is difficult to follow. Give me a second and I will phrase it more accurately.

The real question:

If I have the multiset
{1,1,1,1,1,2,2,2,2,2,4,4,4,4,4,8,8,8,8,8,16,16,16,16,16}

Using 5 of them how many restricted partitions ( order does not count ) can I form?


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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#744 2011-07-02 01:03:52

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Is this cool with you?

Yes, our answers match.


You got this for 6 darts and 5 areas?


"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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#745 2011-07-02 01:09:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Is this cool with you?

Hi gAr;

Yes, the new problem is;

{1,1,1,1,1,1,2,2,2,2,2,2,4,4,4,4,4,4,8,8,8,8,8,8,16,16,16,16,16,16}

The area really means 5 different  types of numbers {1,2,4,8,16}. The 5 types stay the same, the number of them goes up.

Same as yours.


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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#746 2011-07-02 01:14:54

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Is this cool with you?

Hi,

Okay, so you thought of multisets, and I thought of multinomials. Nice!


"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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#747 2011-07-02 01:19:02

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Is this cool with you?

Hi gAr;

When I worked on this for someone else he used pegs on a board. I saw the connection with the restricted partition problem. Not much has been done on them. Everybody knows about partition numbers but when the set is finite then not so much is known.

This is the first improvement I have seen on this type in a while.


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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#748 2011-07-02 01:56:35

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

Okay.
I haven't given multisets much thought.


"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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#749 2011-07-02 02:20:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Is this cool with you?

I have played with them a little. It is harder to find answers to particular ones rather than all of them. The generating function is harder.


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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#750 2011-07-02 02:35:20

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Is this cool with you?

Yeah, I'm still trying for a g.f.


"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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