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 Getting Maps In 2080 (Posted on 2007-08-17)
Let S = {1; 2; 3; 4; 5; 6; 7}

Analytically determine the number of maps f from S to S such that f2080(x) = x for every x belonging to S.

Note: The iteration is denoted by the superscript, such that f1(x) = f(x) and
fn(x) = f(fn-1(x)) for all n > 1.

 Submitted by K Sengupta Rating: 4.3333 (3 votes) Solution: (Hide) 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.

 Subject Author Date one case missing--computer lists all combinations Charlie 2007-08-20 10:36:24 re(2): solution Charlie 2007-08-18 01:14:24 re: solution Federico Kereki 2007-08-17 18:44:22 solution Charlie 2007-08-17 15:34:40

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