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14

Part of 2017 Math Prize for Girls Problems

Problems(1)

Math Prize 2017 Problem 14

Source:

9/26/2017
A permutation of a finite set SS is a one-to-one function from SS to SS. Given a permutation ff of the set {1,2,…,100}\{ 1, 2, \ldots, 100 \}, define the displacement of ff to be the sum ∑i=1100∣f(i)−i∣. \sum_{i = 1}^{100} \left\lvert f(i) - i \right\rvert . How many permutations of {1,2,…,100}\{ 1, 2, \ldots, 100 \} have displacement 4?
Math Prize for Girls