Math Is Fun Forum

gra0001

Member

Registered: 2015-08-10

Posts: 10

Permutation Formula that I cant solve

Can you help me with a permutations calculation
If there was a total of 12 numbers (1,2,3,4,5,6,7,8,9,10,11,12) (n)
I wanted to have a set of 7 numbers (r)
But I ONLY wanted each set to have at least the permutations of 4 numbers and the remaining 3 numbers to not be repeated in any set together but be unique.
SO if ANY of the 4 numbers selected out of the 12 was chosen it would appear in the result.
Thanks in Advance

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Permutation Formula that I cant solve

Can you give an example?

---

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.

gra0001

Member

Registered: 2015-08-10

Posts: 10

Re: Permutation Formula that I cant solve

Someone did it for me 20 Years ago.
It was 12 Numbers and there were 42 sets of 6 numbers
So every number was used 21 times
It covered the Majority of combinations and at least every set of 4 was presented
I am not sure how they got this result?
But I have a problem where I now have to have 7 numbers...it may well take more than 42 sets
Thanks David

1-1,2,3,4,5,6,
2-1,2,3,7,8,9,
3-1,2,3,10,11,12,
4-1,2,4,7,8,10,
5-1,2,4,9,11,12,
6-1,2,5,7,8,11,
7-1,2,5,9,10,12,
8-1,2,6,7,8,12,
9-1,2,6,9,10,11,
10-1,3,4,7,9,10,
11-1,3,4,8,11,12,
12-1,3,5,7,9,11,
13-1,3,5,8,10,12,
14-1,3,6,7,9,12,
15-1,3,6,8,10,11,
16-1,4,5,7,10,11,
17-1,4,5,8,9,12,
18-1,4,6,7,10,12,
19-1,4,6,8,9,11,
20-1,5,6,7,11,12,
21-1,5,6,8,9,10,
22-2,3,4,8,9,10,
23-2,3,4,7,11,12,
24-2,3,5,8,9,11,
25-2,3,5,7,10,12,
26-2,3,6,8,9,12,
27-2,3,6,7,10,11,
28-2,4,5,8,10,11,
29-2,4,5,7,9,12,
30-2,4,6,8,10,12,
31-2,4,6,7,9,11,
32-2,5,6,8,11,12,
33-2,5,6,7,9,10,
34-3,4,5,9,10,11,
35-3,4,5,7,8,12,
36-3,4,6,9,10,12,
37-3,4,6,7,8,11,
38-3,5,6,9,11,12,
39-3,5,6,7,8,10,
40-4,5,6,10,11,12,
41-4,5,6,7,8,9,
42-7,8,9,10,11,12,

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Permutation Formula that I cant solve

Is this for a progressive dinner?

---

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.

gra0001

Member

Registered: 2015-08-10

Posts: 10

Re: Permutation Formula that I cant solve

Nope, not a progressive dinner.
For a project that I am working on.
A formula type game, there is a group of us that use the sample i sent you to increase our chances.
Some of the group are maths teachers...and it has their heads scratching.
But if I could understand why the person who invented it (the sample) with 12 numbers used 42 sets and each number appeared 21 times i could probably sort out how to increase the set to 7 (from 6 numbers)

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Permutation Formula that I cant solve

Hello:

I think I would want more explanation. What is a set of 4?

gra0001

Member

Registered: 2015-08-10

Posts: 10

Re: Permutation Formula that I cant solve

I try to explain better:
So the full 12 numbers are 1,2,3,4,5,6,7,8,9,10,11 and 12
In the reply above I gave the 42 sets of 6 numbers
In that sample each of the 12 numbers ONLY appears 21 times, so this tells me it is a balanced result.

I was to "believe" that in the example EG line 1-1,2,3,4,5,6 that this was only time 1,2,3,4 existed together.
But so does every other set of four permutations in LINE 1 (1,2,3,5 / 1,2,3,6 / 2,3,4,5 / 2,3,4,6 ...etc)
and I call this a set of 4, but because we are extracting 6 numbers and within those 6 we can cover the set of 4 permutations.

Where the normal calculation of having 12 numbers and wanting every combination of 4 is 495 Permutations.
But here we are using a string of 6 numbers but ONLY looking at sets of 4 in it.
It is hard to explain but hope that helps

1-1,2,3,4,5,6,
2-1,2,3,7,8,9,
3-1,2,3,10,11,12,
4-1,2,4,7,8,10,
5-1,2,4,9,11,12,
6-1,2,5,7,8,11,
7-1,2,5,9,10,12,
8-1,2,6,7,8,12,
9-1,2,6,9,10,11,
10-1,3,4,7,9,10,
Etc

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Permutation Formula that I cant solve

Hi;

Line 2)1,2,3,7,8,9, does not contain any 4 permutation from line 1. Why is that?

---

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.

gra0001

Member

Registered: 2015-08-10

Posts: 10

Re: Permutation Formula that I cant solve

Maybe I should say combination not permutations......sorry
If they would call a combination lock a permutation lock...it would of been better for my brain

So line 2 contains a unique set of 4 combinations
Line 2 is 1,2,3,7,8,9 and there is the set of 4 combinations of 1,2,3,7 and 1,2,3,8 and 1,2,3,9 and 2,3,7,8 etc etc
These "may" not exist in any of the other lines of selected numbers of 6
The result is 6 numbers are selected from the 12
Out of those 6 numbers there are combinations of 4 that are not repeated in any other lines.
Just trying to work out a formula that is balanced so each number in the set of 6 is presented the same amount of times.

Maybe it has to be completed manually?

Last edited by gra0001 (2015-08-11 13:59:09)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Permutation Formula that I cant solve

I would guess that the answer given to you was done by computer. I could try to do the same thing for you.

---

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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Re: Permutation Formula that I cant solve

Why do I find this page too messy to read through...

---

'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Permutation Formula that I cant solve

I am not sure I have it yet. The problem is difficult to explain.

---

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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Re: Permutation Formula that I cant solve

Why can't we see examples with much smaller numbers?

---

'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Permutation Formula that I cant solve

How do you mean?

---

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.

gra0001

Member

Registered: 2015-08-10

Posts: 10

Re: Permutation Formula that I cant solve

Hi,
Is there any more info I can pass on?
I hope my explanation will help you to solve the problem.
I think it is a interesting one.
I have an Excel Spread Sheet to send if that helps
David

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Permutation Formula that I cant solve

It seems to me that using combinations of six, each different you want to get all the combinations of four in the shortest number you can?

---

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.

gra0001

Member

Registered: 2015-08-10

Posts: 10

Re: Permutation Formula that I cant solve

Yes, that is what I am after.
And because the current answer all the numbers are used the same time and the spread is balanced.
That is what I am after.
I still think it can only be done manually, but then how to you check to see it is done correctly?
THanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Permutation Formula that I cant solve

You would be counting them up, it is hard to make a mistake doing that.

---

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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Re: Permutation Formula that I cant solve

To present a problem in precise terms is a very very important skill.

---

'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Permutation Formula that I cant solve

Yes it is.

---

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.