Question 167
Two players play the following game: after one of them tells number $n$, the other has to tell a number of the form $a \cdot b$ where $a, b$ are positive integers such that $a + b = n$. The game continues in the same way. If at some point one of the players has told $2011$, which are the possible numbers that the game could have started with?
(Tournament of Towns 2001)
(Tournament of Towns 2001)