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#1 2013-02-19 06:37:06

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 2013-02-19 06:40:01

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 2013-02-19 07:23:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

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 (2013-02-19 14:53:23)


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#4 2013-02-19 23:52:04

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 2013-02-19 23:56:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

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 (2013-02-21 04:50:49)


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#6 2013-02-20 06:16:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#7 2013-02-20 06:33:50

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#8 2013-02-20 06:50:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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

Preety much.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#9 2013-02-20 06:52:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#10 2013-02-20 07:04:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#11 2013-02-20 07:05:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#12 2013-02-20 07:08:23

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#13 2013-02-20 07:16:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#14 2013-02-20 07:21:00

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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

No. n=49 and k=6.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#15 2013-02-20 07:24:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#16 2013-02-20 07:43:20

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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

Hi bobbym

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


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#17 2013-02-20 07:47:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#18 2013-02-20 07:49:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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

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


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#19 2013-02-20 07:50:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#20 2013-02-20 07:53:52

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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

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


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#21 2013-02-20 07:54:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#22 2013-02-20 07:56:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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

I am just running the recurrence.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#23 2013-02-20 07:58:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#24 2013-02-20 07:59:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

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

Yes.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#25 2013-02-20 08:00:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

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