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  •  » Combinations 6 of 49 without the results with numbers in sequence

#1 2013-02-20 05:37:06

Dab Alex
Guest

Combinations 6 of 49 without the results with numbers in sequence

I have a problem I need to solve so I'd need an answer or a way to solve it.
I need to find out the number of combinations of 6 numbers from 49 numbers. The tricky part (for me big_smile)is that I want to exclude the combinations of numbers that are in sequence of minimum 3 meaning:
I want to exclude results like {1,2,3,4,5,6} or like {1,2,3,9,12,14} or {1,2,3,4,6,8} so on....

Thank you!

#2 2013-02-20 05:40:01

Dab Alex
Guest

Re: Combinations 6 of 49 without the results with numbers in sequence

I forgot to mention.... without repetitions and order is not important

#3 2013-02-20 06:23:14

bobbym
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Re: Combinations 6 of 49 without the results with numbers in sequence

Hi;

If order does not count then doesn't {2,46,31,1,5,3} have to excluded? There is a {1,2,3} in there.

Last edited by bobbym (2013-02-20 13:53:23)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#4 2013-02-20 22:52:04

Dab Alex
Guest

Re: Combinations 6 of 49 without the results with numbers in sequence

I mean that the sequence of consecutive numbers must not be contained in the result so this result {2,46,31,1,5,3} must also be excluded.
I specified that order is not important because no. of combinations if order is important is 1.00683475e+10 and if it isn't no. of combinations is 13983816

#5 2013-02-20 22:56:52

bobbym
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Re: Combinations 6 of 49 without the results with numbers in sequence

Hi;

Yes, you are correct there are 10068347520 permutations and only 13983816 combinations.

I think I have enough to start working on it, thanks.

I am getting that 13316842 out of 13983816 do not have 3 or more numbers in sequence. This agrees well with simulations.

Last edited by bobbym (2013-02-22 03:50:49)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#6 2013-02-21 05:16:49

anonimnystefy
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Re: Combinations 6 of 49 without the results with numbers in sequence

I think the reccurence is:

A(n,k)=A(n-3,k-2)+A(n-2,k-1)+A(n-1,k), n>3, with the appropriate starting conditions.


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

#7 2013-02-21 05:33:50

bobbym
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Re: Combinations 6 of 49 without the results with numbers in sequence

Hmmmm? Are you sure?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#8 2013-02-21 05:50:59

anonimnystefy
Real Member

Offline

Re: Combinations 6 of 49 without the results with numbers in sequence

Preety much.


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

#9 2013-02-21 05:52:43

bobbym
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Re: Combinations 6 of 49 without the results with numbers in sequence

What are your initial conditions?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10 2013-02-21 06:04:57

anonimnystefy
Real Member

Offline

Re: Combinations 6 of 49 without the results with numbers in sequence

A(n,k) is 0 for n<=0, except A(0,0)=1.


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

#11 2013-02-21 06:05:41

bobbym
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Re: Combinations 6 of 49 without the results with numbers in sequence

You also did not define n or k. What are they?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#12 2013-02-21 06:08:23

anonimnystefy
Real Member

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Re: Combinations 6 of 49 without the results with numbers in sequence

Numbers, of course.

Joke aside, n is how many numbers we choose from and k is how many numbers we choose.


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

#13 2013-02-21 06:16:13

bobbym
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Re: Combinations 6 of 49 without the results with numbers in sequence

k is how many numbers we choose.

You are saying n=6 and k is the number of consecutives?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#14 2013-02-21 06:21:00

anonimnystefy
Real Member

Offline

Re: Combinations 6 of 49 without the results with numbers in sequence

No. n=49 and k=6.


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

#15 2013-02-21 06:24:59

bobbym
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Re: Combinations 6 of 49 without the results with numbers in sequence

Did you check it by actually running the recurrence? Does it get my answer?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#16 2013-02-21 06:43:20

anonimnystefy
Real Member

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Re: Combinations 6 of 49 without the results with numbers in sequence

Hi bobbym

Sorry. Take A(0,1)=1 as well.


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

#17 2013-02-21 06:47:37

bobbym
Administrator

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Re: Combinations 6 of 49 without the results with numbers in sequence

Hi;

The same question as the last post. Did you try it?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#18 2013-02-21 06:49:12

anonimnystefy
Real Member

Offline

Re: Combinations 6 of 49 without the results with numbers in sequence

I'm calculating it. It will take a while.


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

#19 2013-02-21 06:50:52

bobbym
Administrator

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Re: Combinations 6 of 49 without the results with numbers in sequence

That is like music to my ears!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#20 2013-02-21 06:53:52

anonimnystefy
Real Member

Offline

Re: Combinations 6 of 49 without the results with numbers in sequence

Do you think there is a way to speed it up?


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

#21 2013-02-21 06:54:57

bobbym
Administrator

Offline

Re: Combinations 6 of 49 without the results with numbers in sequence

I do not know what you are doing, so how can I say.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#22 2013-02-21 06:56:56

anonimnystefy
Real Member

Offline

Re: Combinations 6 of 49 without the results with numbers in sequence

I am just running the recurrence.


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

#23 2013-02-21 06:58:15

bobbym
Administrator

Offline

Re: Combinations 6 of 49 without the results with numbers in sequence

That is what I mean. In Maxima?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#24 2013-02-21 06:59:07

anonimnystefy
Real Member

Offline

Re: Combinations 6 of 49 without the results with numbers in sequence

Yes.


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

#25 2013-02-21 07:00:35

bobbym
Administrator

Offline

Re: Combinations 6 of 49 without the results with numbers in sequence

Well, when I ask this question the kaboobly doo will hit the fan. Where does it come from?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
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