TR-MO-R1 2012 Problem 4

$A = \{1,2,3,4,5,6,7\}$ kümesinin tüm $a$ elemanları için $f(f(a)) = a$ koşulunu sağlayan kaç $f : A \to A$ fonksiyonu vardır?

a) 1 b) 106 c) 127 d) 232 e) Hiçbiri

Official text Turkish Mathematical Olympiad, first round 2012 official paper, page 2. Quoted with source.

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