# Permutations: A Very Simple Perspective ## Examples We have a simple solution for \( n = 4 \). It is \[ 2, 4, 1, 3. \] For \( n = 5 \), we just append \( 5 \) to the previous solution: \[ 2, 4, 1, 3, \underset{\uparrow}{5}. \] For \( n = 6 \), we insert \( 6 \) between the last even number and the first odd number: \[ 2, 4, \underset{\uparrow}{6}, 1, 3, 5. \] ## Generalization Let the solution for \( n = 4 \) be \[ 2, 4, 1, 3. \] For odd \( n \), append \( n \) to the solution for \( n - 1 \): \[ 2, \dots, (n - 1), 1, \dots, (n - 2), \underset{\uparrow}{n}. \] For even \( n \), insert \( n \) between \( n - 2 \) and \( 1 \): \[ 2, \dots, (n - 2), \underset{\uparrow}{n}, 1, \dots, (n - 1). \]