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2017 MPFG Problem 14

Revision as of 08:13, 22 October 2025 by Cassphe (talk | contribs) (Created page with "==Problem== A <math>\textit{permutation}</math> of a finite set <math>S</math> is a one-to-one function from <math>S</math> to <math>S</math>. Given a permutation <math>f</mat...")
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Problem

A $\textit{permutation}$ of a finite set $S$ is a one-to-one function from $S$ to $S$. Given a permutation $f$ of the set ${1,2,...,100}$, define the displacement of $f$ to be the sum $\sum_{i=1}^{100}\left|f(i)-i\right|$. How many permutations of ${1,2,...,100}$ have displacement $4$?

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