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Number of $f$ for which $f(f(x))$ is constant

Source: AIME II 2013, Problem 11

April 4, 2013
functionAMCAIMEAIME IIcombinatorics

Problem Statement

Let A={1,2,3,4,5,6,7}A = \left\{ 1,2,3,4,5,6,7 \right\} and let NN be the number of functions ff from set AA to set AA such that f(f(x))f(f(x)) is a constant function. Find the remainder when NN is divided by 10001000.
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