Problem

Source:

Tags: combinatorics



$100$ people came to the party. Then those who had no acquaintances among those who came left. Among those who remained, then those who had exactly $1$ friend , also left. Then those who had exactly $2$, $3$, $4$,$ . .$ , $99$ acquaintances among those remaining at the time of their departure did the same..What is the largest number of people left at the end?