Re: Help: How to combine all 4's into least 6's- Is there a way to calculate what the minimum of 6's will be?


gnh888@xxxxxxxxx wrote:
> Hello
>
> What is the algorithm or principle to combine all the combinations of
> 4s
> into the smallest combination of 6s from a range of 10 consecutive
> numbers?
>
> Is there a way to calculate what the minimum 0f 6 numbers will be
> before doing it?
>
> The data is below.
>
> The set of 10 numbers are { 1,...,10}.
>
> There are 210 subsets of 4 numbers [a,b,c,d] in this set of 10 numbers
>
> I want to find the lowest number of subsets of 6 numbers
> [a,b,c,d,e,f,g]
> which
> will contain all the subset of 4's[a,b,c,d]
>
> 21 is the minimum number of subsets of 6 numbers [a,b,c,d,e,f,g] which
> will contain all the subset of 4's[a,b,c,d] _ see below what my result
> is?
>
> I used brut force to get the result but I am not sure 21 subsets of 6's
> is the lowest?
>
> I am talking here about an algorithmic process which I can understand.
>
> Please spare my brain and if you can be really down to earth , thanks?
> an be then written in Basic,
>
> Then I can write from what your explanation my version in Basic, C,
> C++, Java etc
>
>
> 1) How does the algorithm works to find the minimum of number of
> subsets
>
> 2) Is it possible to use matrices to resolve this problem? and how?
>
> 3) Any websites, and information appreciated
> ==
> Explanation:
> Combinations of 4's or set of 4's
> [1 2 3 5], [1 2 3 5], [ 1 2 3 6], ....,[6 7 9 10], [6
> 8 9
> 10], [7 8 9 10]
> (please - no permutations)
>
> Combinations of 6's or set of 6's
> [1 2 3 4 5 6], [1 2 3 4 6 7],....,[5 6 7 8 9 10]
>
> Expected result below of 21 sets of 6's or better than below ( better
> means less than 20 sets of 6's)
>
> 4) My results for grouping all 4s into the least number
> of combinations of 6s .
> I find 21 combinations of 6s?
>
> But what I am after is the way you set up the algorithm or explain how
> it works
> without using brut force?
> 1 1 2 3 4 5 6
> 2 1 2 3 4 7 8
> 3 1 2 3 4 9 10
> 4 1 2 4 5 7 10
> 5 1 2 4 6 8 9
> 6 1 2 5 6 7 9
> 7 1 2 5 6 8 10
> 8 1 3 5 6 7 8
> 9 1 3 5 6 9 10
> 10 1 3 7 8 9 10
> 11 1 4 5 8 9 10
> 12 1 4 6 7 9 10
> 13 2 3 4 5 8 10
> 14 2 3 4 6 7 9
> 15 2 3 5 7 9 10
> 16 2 3 6 8 9 10
> 17 2 4 5 7 8 9
> 18 2 4 6 7 8 10
> 19 3 4 5 6 7 10
> 20 3 4 5 6 8 9
> 21 5 6 7 8 9 10


Didn't you make another post showing a set of 20, or was I
halucinating?

Anyway, I got a program that finds a 21 set solution. It's running
overnight to see if I can get a better set. I'll post results tomorrow.

.

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