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Getting Maps In 2080 (Posted on 20070817) 

Let S = {1; 2; 3; 4; 5; 6; 7}
Analytically determine the number of maps f from S to S such that
f^{2080}(x) = x for every x belonging to S.
Note: The iteration is denoted by the superscript, such that
f^{1}(x) = f(x) and f^{n}(x) = f(f^{n1}(x))
for all n > 1.
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