Macro to return columns as described in the post

[Asth]

Hello. I've posted this in the part of the forum about formulas, but I'm starting to doubt that there is such a formula, so here's my question again, exemplified.

I have a table of 36x36 containing values of 1's and 0'2, plus a 37th column that has the sums of each row. (example of 6X7 below, 7th column being the one containing the sums)

ABCDEF G
010101 3
010011 3
010101 3
001011 3
001101 3
001011 3

I need to know if there's a macro out there that can help me by returning the following: every possibility (combination) of column summing that would make the entire 7th column have ONLY even or ONLY odd results.

For the example above, possibilities for even results are:
A
A+B+C+D+E
A+B+C+F
B+C+D+E
B+C+F

For odd results:
A+B+C+D+E+F
A+B+C
A+D+E
A+F
B+C+D+E+F
B+C
D+E
F

If there is no such macro, is there any way of creating a program, or anything similar?

Thank you in advance.
Asth.

[ragulduy]

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Something like that might do it. It would take FOREVER though. You would be looking at billions of possible combinations.

Disclaimer: untested obviously. It may or may not work!
I don't think there is a way to do this that isn't brute force though, unless there is some pattern to your numbers.

I reckon it's a fair bet that are part from trivial solutions (all zero's or single 1's in each line) there aren't going to be any others.

[Asth]

I'll try this out as soon as I get home, thanks! The only pattern I've seen in my table is that column A = row 1; column B = row 2; and so on. I know there can be quite a lot of possibilities, however I have a feeling there are only 2 valid. :P Thanks again. I'll get back to you with results. (or further questions)

[ragulduy]

Haha, I wouldn't be in such a rush. It was more an example of how you would approach it but scaled up to 36x36, even as a conservative estimate you would be looking at like, a month to run something like that.

How are your numbers populated? are they all 1's and 0's? What do you need the information for?

[Asth]

They represent a puzzle. If you look at the puzzle, it's a circle with symbols on it. Each symbol activates some others, therefor for symbol 1, I add one to each of the symbols it affects. I need them all activated, thus, the results need to be all even or all odd. :P

[Asth]

Sorry, I wrote that in a hurry. If I get into it more, it sounds like this.

There are 36 symbols. Each activates a number of other symbols. (4, 6 or 9 others) So, for example, if symbol 1 activates symbols 5, 13, 27 and 33, then column A will have 1's on rows 5, 13, 27, 33, and 0's for the rest 32 symbols. (numbers) After turning the puzzle into an excel project, I noticed that the upper right side is a mirror of the lower left one, so there's a diagonal of 1's from A1 to AJ36. I figured it's all just a form of complex math that could be simplified by a macro or formula, but I might have been wrong. :P I've tried to think of it in a C++ form either by turning it into 36 matrices of 1x36, or by using it as a single 36x36 matrix. Considering I haven't used any programing in well over 6 years, I failed miserably. So I turned to help here.

[Asth]

Another thing I tried but was unable to, was to think of the matter the following way:

C <- combinations
n = no. of columns
k <= n
c(x) column 1 through x
x = 1 through 36

So I tried to figure a way that would tell me if c(37) = (C of n by k (sum of c(x))) is either odd or even. I have no idea how to convert that into code, though...

[ragulduy]

I don't quite see how what your asking for will help you with the puzzle but anyway... I take it the goal is to have the symbols on?

It sounds like a variation of "lights out". If you do a google search for "lights out solving algorithm" or something along those lines there is loads of stuff available on these sorts of problems.

[Asth]

That information was golden. It is indeed that type of puzzle. 4 corners (4 tiles affecting 4 others) 16 margins (4x4 affecting 6 others) and 16 in the center. (4x4 affecting 9 others) After that it went down simple rearranging and figuring out. Consider this topic solved from my point of view, although my idea didn't really have an ending. :P And thank you very much for ending my torment. :P