Generate all binary combinations with constant sums of rows and columns

B

bekirsahin

New Member
Joined
Feb 28, 2018
Messages
5
I have a problem regarding to excel binary combinations. As you see there is a matrix (Matrix 1) with the values of 1 and 0. --- represents N/A or 0. I want to get all different combinations without changing the sums.

Matrix 1:
[TABLE="class: grid, width: 500, align: center"]
<tbody>[TR]
[TD="align: center"][/TD]
[TD="align: center"][/TD]
[TD="align: center"][/TD]
[TD="align: center"][/TD]
[TD="align: center"][/TD]
[TD="align: center"][/TD]
[TD="align: center"]Sum[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]2[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]4[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]2[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]2[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]2[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]3[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]3[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]2[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]4[/TD]
[/TR]
[TR]
[TD="align: center"]Sum[/TD]
[TD="align: center"]7[/TD]
[TD="align: center"]6[/TD]
[TD="align: center"]6[/TD]
[TD="align: center"]3[/TD]
[TD="align: center"]2[/TD]
[TD="align: center"]24[/TD]
[/TR]
</tbody>[/TABLE]


For example, below is a different combination of the Matrix 1. Red ones are the only changed numbers and the sums never changed.

[TABLE="class: grid, width: 500, align: center"]
<tbody>[TR]
[TD="align: center"][/TD]
[TD="align: center"][/TD]
[TD="align: center"][/TD]
[TD="align: center"][/TD]
[TD="align: center"][/TD]
[TD="align: center"][/TD]
[TD="align: center"]Sum[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]2[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]4[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]2[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]2[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]2[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]3[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]3[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]0[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]2[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]1[/TD]
[TD="align: center"]---[/TD]
[TD="align: center"]4[/TD]
[/TR]
[TR]
[TD="align: center"]Sum[/TD]
[TD="align: center"]7[/TD]
[TD="align: center"]6[/TD]
[TD="align: center"]6[/TD]
[TD="align: center"]3[/TD]
[TD="align: center"]2[/TD]
[TD="align: center"]24[/TD]
[/TR]
</tbody>[/TABLE]



I appreciate your effort.

Thank you very much
Sincerely
 

Excel Facts

Whats the difference between CONCAT and CONCATENATE?
The newer CONCAT function can reference a range of cells. =CONCATENATE(A1,A2,A3,A4,A5) becomes =CONCAT(A1:A5)
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