# Permutations: Yet Another Perspective ## Odd \( n \), Start With \( 1 \) Example: \( 1, 3, 5, 2, 4 \). General: \( 1, \dots, n, 2, \dots, (n - 2) \). Works for: \( n \ge 4 \implies n \ge 5 \). ## Odd \( n \), Start With \( 2 \) Example: \( 2, 4, 1, 3, 5 \). General: \( 2, \dots, (n - 2), 1, \dots, n \). Works for: \( (n - 2) \ge 3 \implies n \ge 5 \). ## Even \( n \), Start With \( 1 \) Example: \( 1, 3, 5, 2, 4, 6 \). General: \( 1, \dots, (n - 1), 2, \dots, n \). Works for: \( (n - 1) \ge 4 \implies n \ge 5 \implies n \ge 6 \). ## Even \( n \), Start With \( 2 \) Example: \( 2, 4, 6, 1, 3, 5 \). General: \( 2, \dots, n, 1, \dots, (n - 1) \). Works for: \( n \ge 3 \implies n \ge 4 \). ## Summary * Start with \( 1 \): Works for \( n \ge 5 \). * Start with \( 2 \): Works for \( n \ge 4 \).