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Basically Math::Combinatorics returns a list as output.
Why not get two list from two different sets, and then merge and shuffle them?
The same name on every site (unless it is taken already)
A different name for every site
The same name for sites I don't care about, but different names on sites I do care about
Different names for sites I don't care about, but the same name on sites I do care about
The anonymous account
Someone else's username
Root, after hacking into the site
Results (257 votes),