Lesson 1

In this section, we prove that exchanging \(14\) and \(15\) in the 15 Puzzle is impossible. To do this, we will be looking at permutations of integers \(\{0, 1, \dotsc, n-1\}\) and we assume that they are indiced by the same integers. A transposition in a permutation \(\pi\) is an exchange of two different elements of \(\pi\).