Suppose there are 10 people who live in different cities. And I want to know who lives where. Each time I can ask two of them 'who of you lives closer to X?' Where X is myself or another person of the group.
Is it possible to calculate the approximate locations of those 10 people with those restrictions? And if not, what questions could I ask them to be able to deduce their location without asking directly?
At the extreme, you can ask all $\frac 12(10)(11)$ pairs to compare their distances. Assuming no city-city distances match, you can match that list to the sorted list of distances between the cities and know where everyone is. The obvious improvement is to try to find a smaller set of comparisons that will also let you match people to cities. I suspect that depends on where the cities are. If one is very far from all the rest, it should be easy to identify the person who lives there.