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Beautiful arrangements

Source: Indonesia Mathematics Olympiad 2007 Day 1 Problem 4

June 2, 2008
combinatorics proposedcombinatorics

Problem Statement

A 10-digit arrangement 0,1,2,3,4,5,6,7,8,9 0,1,2,3,4,5,6,7,8,9 is called beautiful if (i) when read left to right, 0,1,2,3,4 0,1,2,3,4 form an increasing sequence, and 5,6,7,8,9 5,6,7,8,9 form a decreasing sequence, and (ii) 0 0 is not the leftmost digit. For example, 9807123654 9807123654 is a beautiful arrangement. Determine the number of beautiful arrangements.
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