I have the numbers 0-8 so I can represent a state as
012345678
012345687
....
876543201
876543210
This gives me 40320 ways to represent a state so I have a HashMap of size 40320 and I need a good way to make sure each state only corresponds to 1 key 1-40320

I'm not really sure how to even come close to making sure there are no possible collisions. Any help would be greatly appreciated

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HashMap should be clever enough to do a rehash in case of a collision.

Since your problem is one of permutations, using an array and something like this will let you generate the arrangement as you need it.

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