HMMT November 2024 T6

There are 5 people who start with $1,2,3,4$, and 5 cookies, respectively. Every minute, two different people are chosen uniformly at random. If they have $a$ and $b$ cookies and $a \neq b$, the person with more cookies eats $|a-b|$ of their own cookies. If $a=b$, the minute still passes with nothing happening.

Compute the expected number of minutes until all 5 people have an equal number of cookies.