"In Newtonian Mechanics, the three-body problem involves the challenge of trying to model as a function of time the orbital path of three free floating gravitationally bound objects orbiting around each other. It's a common problem in astrophysics, and there are interesting things that result from it. If you study Lagrange points, you'll realize how these things are useful, especially for satellites.
The two-body problem is slightly different. In the two-body problem, you have a couple, a husband and wife, or boyfriend and girlfriend, or any other pair, and both of them are in science. Unfortunately, one of them gets a post-doc position in Hawaii and the other one ends up at an European Observatory. The two-body problem deals with trying to reconcile this problem.
The one-body problem is similar to the two-body problem... except you're trying to find the second body. It's a tough problem... so many technicalities and circumstances to work out. It's probably just timing"