perplexus.info :: Just Math : Getting Maps In 2080

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(f^n-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.

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

Comments: ( You must be logged in to post comments.)

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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