Let's say there are doors each with a lock on the integral points ($0$, $\pm1$, $\pm2$, $\cdots$) of the line. You are given a key which can only open a single lock, but you are not told what lock the key is for. Your goal is to find the correct lock and open that door. Initially you are at origin. How can you come up with a strategy to minimize $d/n$ in the worst case, where $d$ is the distance you will be walking in total following that strategy, and $n$ is the distance of the matched door to this given key from origin.
Does anybody here see this problem before? Please give some of your thoughts and solutions.