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Combinatorial design problem 
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#1
Nov1312, 12:36 PM

P: 79

Hey!
I have a certain problem. Let M ≥ 4 be an even number and consider the set [0,1,...[itex]\frac{M}{2}[/itex]1]. The problem is to put those numbers two times in each row of an M x (M choose 2) matrix, such that all possible combinations of entries that contain a pair of the same number occur just once. For example, M = 4 it can be trivially seen that the matrix will be: [0 0 1 1; 0 1 0 1; 0 1 1 0; 1 0 0 1; 1 0 1 0; 1 1 0 0] Indeed all possible combinations of entries that contain 0 in a row, occur just once. This is also true for all possible combinations of entries that contain the number 1. For M = 6 though, things get much more difficult. Is there an algorithm that can produce such matrices for arbitrary M? Does such a matrix even exist? Any papers or other info? Thanks! 


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