Find Best Combinations of Non-Overlapping Matrix Elements

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JeffreyP
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Algorithm for finding best (or combinations of) "non-overlapping" matrix elements.

I'm looking for the best general way to find the "best" combination for a list of non-overlapping matrix elements. For example, given the matrix

AE BE CE DE
AF BF CF DF
AG BG CG DG
AH BH CH DH

The combination of values that results in the highest sum, but where no letter appears more than once.
 
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JeffreyP said:
The combination of values that results in the highest sum, but where no letter appears more than once.

Sum of what? Are you talking about a situation where the matrix really has 3 items per entry, these being a number and two letters? - such a (93.6,A,E)