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My brain hurts, but I "think" you may have it nailed

The trick is to have ALL the 4 Combinations contained in minimum of 6 numbers

Some 4 combinations will appear more than once but that has to be.

Can be written in anything!

I could try but I don't know what the terms are

Trust me I have looked and looked for examples

Thought I would ask here, as I always use the www link to create the "combinations"

I have an Excel that I use that displays where the 4 combinations are found in the 6 numbers

And at the end I export a CSV file of the 6 numbers

**gra0001**- Replies: 7

Hi, looking for a person to program or maybe use VBA in Excel to Solve something.

Lets say I have 12 Numbers 1 to 12, so there are 495 sets of 4 combinations

Sample: Using this link (below) and Selecting 12 numbers and 4 numbers to choose

Is Order important?= No Is Repetition allowed?=No

https://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html

Now I want to list the minimum number of 6 number sets that contain the 4 number combinations

Manually I worked out I could do it in 42 sets of 6 numbers that contained all 495 combinations

That is we would have all the 4 combinations in a set of 6 numbers of the 12 numbers.

I don’t know what you call this Subsets?

EG The 12 Numbers are 1,2,3,4,5,6,7,8,9,10,11,12

There are 495 combinations of 4 numbers

-In say 1,2,3,4,5,6 (6 Numbers) there are 15 Combinations of 4

(1,2,3,4)(1,2,3,5)(1,2,3,6)(1,2,4,5)(1,2,4,6)(1,2,5,6)(1,3,4,5)(1,3,4,6)(1,3,5,6)(1,4,5,6)(2,3,4,5)(2,3,4,6)(2,3,5,6)(2,4,5,6)(3,4,5,6)

-In say 1,2,3,7,8,9 (6 Numbers) there are 15 combinations of 4

(1,2,3,7)(1,2,3,8)(1,2,3,9)(1,2,7,9)(1,2,8,9)(1,3,7,8)(1,3,8,9)(1,7,8,9)(2,3,7,8)(2,3,7,9)(2,7,8,9)(3,7,8,9)(1,3,7,9)(2,3,8,9)(1,2,7,8)

So in 42 Lines of sets of 6 number combinations I created a list that contain all 495 combinations of 4

42 Lines was the minimum, and I believe the sets of 6 was balanced because I used each number in the set of 6 numbers 21 times each

The Program I need is:

Enter the Total number of Numbers EG 12 (But can be any number to 50)

Enter the Total number used in each SET EG 6 (But can be any number to 10)

Enter the Total number of Combinations to cover EG 4 (But can be any number to 10)

Then display 2 things:

-The string of the 6 Numbers (1 Row for every set of 6 numbers)

-All the Combinations of 4 and what row they appear in (for error checking)

-Note: It needs to be done in the Minimum of Rows of 6 numbers

Yes some duplication of obtain the 4 combinations may happen as it did in my 42 set of 6

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

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

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?

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

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)

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,

**gra0001**- Replies: 19

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

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