Question 61
The Retired Linguist (R.L.) in his first move writes a word consisting of $n$ distinct letters in his notebook. Thereafter, in each move he writes a new word in the notebook, obtained by reversing the longest sub-word (starting from the first letter) of the last added word, provided the resulting word has not been written in the notebook before. Show that R.L. will write $n!$ words in his notebook.