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Apologies for my silly question, I'm still at the beginning of my journey, but shouldn't the odd and even cases evaluate to the same value if you replace "n" by "n-1" in the right hand side of (2) ? Since the calculation we do for the odd case is exactly the calculation for the even case of the number one less than n? So if you name the sum/product S(n) then S(5) should equal S(4) for example? Or what am I missing?
The only way I could see this contributing additional information is if the assistant hands you the 4 smallest cards (you could order the suits too) but that only takes it down to 44 in the worst case scenario, I wonder if someone can think of a better method