1. I'm looking for a better than method.

I have "objects" and "things". I can not order my "objects" or "things" but when I pair an "object" with a "thing" I can calculate a number . I need to know what combination of pairs of "objects" and "things" will minimize

The poor method.
1) Assign a number to each of the "objects"
2) Calculate for all possible orders of "things"
3) pick the order that gave the least

Physical example:
I have 5 odd shapes of blue paper and 5 odd shapes of red paper. Every shape has the same area. (i.e I can't assign an order to the shapes)
When I place a red shape on top of a blue shape I can calculate the area of blue that is not coved by the red shape. This is the

Any idea may help.

2.

3. Actually, you can do it in by just checking each object vs each thing, and storing the results in an n-by-n table. Checking the ways of ordering the things would generate a lot of duplicated checks. Off hand, I don't think you'd be able to reduce it below without some details from the specific problem.

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