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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.

Submitted by K Sengupta

Rating: 4.3333 (3 votes)


Solution:

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The required number of maps is 2080.
A detailed explanation of the foregoing is furnished in Problem Number 2080 of journalsDotcmsDotmathDotca in this location.

For an alternative method, refer to the comments posted by Charlie in the comments section.

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