Originally posted by Atlas
This does seem strangely possible. The first city point is picked arbitrarily on a blank piece of paper. Then 9 circles of varying radii signifying the possible locations of the other 9 cities at the proper distance to city1.
Then arbitrarily choose a point for city2 somewhere on the appropriate circle drawn around city1, and draw 9 more circles with radii appropriate for the distances from city2 to the other 9 cities.
I'm trying to imagine if that is enough. Would the intersecting circles around City1 and City2 identify the locations of the other 8 cities? I think it would.
[edit] I just reread Vorticity's solution. There will be a choice of two points for each of the cities, won't there? But selecting the 3rd city's position arbitrarily from the 2 available choices and drawing 9 more circles should definitively give you the relative locations of all the cities. And my answer is the same as his, darn it! [/edit]
