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Gordon Shumway: The ability to leave an empty spot is identical to adding another colour.
The general formula for the number of codes with N spots and C colours is CN for regular logic; for unique logic, the formula is C!/(C-N)!, assuming there are at least as many colours as there are spots (otherwise, you wouldn't have any possible codes).
AbigailII: So Unique Logik with two additional colors seems to be roughly in the same range of complexity as our current Logik - I think I'd like it :)