I have n buckets and mn entities. Each bucket must have m entities. Each
entity carries a weight. My objective is to even out the total weight per
bucket, make them close to the average.

For example, a solution like this is skewed, see their sums.
bucket 1: 1,2,4,5=12
bucket 2: 6,8,9,6=29
bucket 3: 7,7,4,7=25

The same entities may be placed into buckets like this. This is more
desirable as the sums are closer to the mean (and each other); one does not
dominate the others.
bucket 1: 1,8,7,4=20
bucket 2: 6,2,9,6=23
bucket 3: 7,7,5,4=23

*Question:*How do I write a rule for this:
for each bucket, penalize (with soft scores) a bucket whose total
entity.weight differs from the average total entity.weight of the buckets.

Will I get the same results when I penalize each bucket for differing with
*each other*?

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