B Finding all possible sums given 2 lists, matched one to one

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To find all possible sums from two lists of numbers, A and B, where each element can only be used once, one must consider the permutations of the lists. The total number of permutations is calculated as n!, but this number is reduced due to repeated elements in the lists. The challenge lies in accounting for these duplicates to avoid counting the same sum multiple times. The user seeks guidance on efficiently calculating these sums, potentially using a spreadsheet for analysis. Ultimately, the goal is to explore all unique combinations of sums derived from the two lists.
mishima
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Hi, its been a while since I have thought about this type of math, and I can't really remember how to do this or what its even called. I have two lists of numbers:

A: 8, 8, 9, 10, 7, 8
B: 6, 5, 4, 3, 3, 3

I want to find all the different ways I can add elements from A with elements of B. For instance, just adding them vertically as they are here I could get one combination as:

C: 14, 13, 13, 13, 10, 11

When an element from a list is used, its gone. For example, if I added 10 from A and 6 from B, I can't use 6 again (or vice versa). Can anyone nudge me in the right direction?
 
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The number of ways you can pick an entry in the A list to be added to an entry in the B list is the number of permutations, which is n! This number will be reduced by the fact that many of the sums are the same, which feels like a hard problem to handle.
 
Ok, so 720 possibilities. I could've sworn there was a way to account for repeats but like I said it has been a while since I have touched on this style of thinking. Ultimately I am just trying to make a spreadsheet to crunch it all out.
 
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