MathDB

Math Prize 2017 Problem 14

Source:

September 26, 2017

Math Prize for Girls

Problem Statement

A permutation of a finite set

S

is a one-to-one function from

S

to

S

. Given a permutation

f

of the set

\{ 1, 2, \ldots, 100 \}

, define the displacement of

f

to be the sum

\sum_{i = 1}^{100} \left\lvert f(i) - i \right\rvert .

How many permutations of

\{ 1, 2, \ldots, 100 \}

have displacement 4?

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