Erdos posed the following question: Let be the min number of distinct distances that you can get with points in . Try to find asymptotically. For example, if (the most studied case), this amounts to two questions: (1) How can you place points in the plane to minimize how many different distinct distances there are, and (2) Given any set of points in the plane, how many distinct distances are you guaranteed.

N. Katz and G.Tardos. Contemporar Mathematics Volume 342. . Exp is approx 0.8641]