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Getting Maps In 2080 (Posted on 2007-08-17) Difficulty: 4 of 5
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.

See The Solution Submitted by K Sengupta    
Rating: 4.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re: solution | Comment 2 of 4 |
(In reply to solution by Charlie)

Why do you say there cannot be cycles of length greater than 7? If you had a 3-cycle and a 4-cycle, the total cycle length would be 12.
  Posted by Federico Kereki on 2007-08-17 18:44:22

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