Question 62
Let $n$ be Tracey's favourite positive integer. Suppose that her opponent initially writes a certain positive integer $m$ on the blackboard and that whenever a positive integer $a$ is already written on the blackboard then Tracey is permitted to also write the numbers $17 \cdot a$ and $[\sqrt{a}]$ on it. Prove that whichever number her opponent selects in the beginning, Tracey can always achieve that $n$ appears on the blackboard as well.