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Number of one-to-one function

Source: Korea National Olympiad 2009 Problem 5

September 9, 2012
functioncombinatorics proposedcombinatorics

Problem Statement

Let A={1,2,3,⋯ ,12} A = \{ 1, 2, 3, \cdots , 12 \} . Find the number of one-to-one function f:A→A f :A \to A satisfying following condition: for all i∈A i \in A , f(i)−i f(i)-i is not a multiple of 3 3 .
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