BrowserUk,
I am just now getting a chance to look at this. While I haven't had an opportunity to implement my heuristic algorithm outlined above, brute forcing it should be in the realm of possibility. 
186 Choose 6 = 53,011,617,022

[download]

See Arbitrarily Nested Loops where I indicated I could get 25-30 million iterations per second using a modest windows machine (albeit in C). That makes checking all possible combinations in about 35 minutes. Of course, not all possible combinations need to be checked because every item you choose reduces the possible choices (can't undershoot or overshoot the target sum). I am a terrible C programmer and could not make a generic interface though ikegami gave it a go.

Since I don't really understand the OP's objective (I readily admit to having only skim read the original thread), I am not sure what approach to go with. My inclination would be a heuristic solution that almost always produces an acceptable solution though not always the best versus and exhaustive search that short circuits when it has found an acceptable solution or an exhaustive search that finds all possible acceptable solutions.

Cheers - L~R

In reply to Re^3: Bin packing problem variation repost (see[834245]) by Limbic~Region
in thread Bin packing problem variation repost (see[834245]) by BrowserUk

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