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Number of good permutations

Source: 2022 Bulgarian Spring Math Competition, Problem 10.3

March 27, 2022
combinatoricsPermutations with restrictions

Problem Statement

A permutation σ\sigma of the numbers 1,2,…,101,2,\ldots , 10 is called <spanclass=′latex−italic′>bad</span><span class='latex-italic'>bad</span> if there exist integers i,j,ki, j, k which satisfy 1 \leq i < j < k \leq 10   \text{ and }  \sigma(j) < \sigma(k) < \sigma(i) and <spanclass=′latex−italic′>good</span><span class='latex-italic'>good</span> otherwise. Find the number of <spanclass=′latex−italic′>good</span><span class='latex-italic'>good</span> permutations.
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