Combinations 6 of 49 without the results with numbers in sequence

Dab Alex · 2013-02-19 06:37:06

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 )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!

Dab Alex · 2013-02-19 06:40:01

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

bobbym · 2013-02-19 07:23:14

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)

Dab Alex · 2013-02-19 23:52:04

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

bobbym · 2013-02-19 23:56:52

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)

anonimnystefy · 2013-02-20 06:16:49

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.

bobbym · 2013-02-20 06:33:50

Hmmmm? Are you sure?

anonimnystefy · 2013-02-20 06:50:59

Preety much.

bobbym · 2013-02-20 06:52:43

What are your initial conditions?

anonimnystefy · 2013-02-20 07:04:57

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

bobbym · 2013-02-20 07:05:41

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

anonimnystefy · 2013-02-20 07:08:23

Numbers, of course.

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

bobbym · 2013-02-20 07:16:13

k is how many numbers we choose.

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

anonimnystefy · 2013-02-20 07:21:00

No. n=49 and k=6.

bobbym · 2013-02-20 07:24:59

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

anonimnystefy · 2013-02-20 07:43:20

Hi bobbym

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

bobbym · 2013-02-20 07:47:37

Hi;

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

anonimnystefy · 2013-02-20 07:49:12

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

bobbym · 2013-02-20 07:50:52

That is like music to my ears!

anonimnystefy · 2013-02-20 07:53:52

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

bobbym · 2013-02-20 07:54:57

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

anonimnystefy · 2013-02-20 07:56:56

I am just running the recurrence.

bobbym · 2013-02-20 07:58:15

That is what I mean. In Maxima?

anonimnystefy · 2013-02-20 07:59:07

Yes.

bobbym · 2013-02-20 08:00:35

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

Math Is Fun Forum

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

Combinations 6 of 49 without the results with numbers in sequence

#2 2013-02-19 06:40:01

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

#3 2013-02-19 07:23:14

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

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

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

#5 2013-02-19 23:56:52

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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