Question 5
Fix an integer $n\ge3$. Initially the number $1$ is written $n$ times on a blackboard, and two buckets are empty. A move erases two numbers $a,b$, replaces them by $1,a+b$, adds one stone to the first bucket, and adds $\gcd(a,b)$ stones to the second. After finitely many moves the buckets contain positive integers $s,t$ stones. Find all possible values of $t/s$.