Don't think you ever find out what 101's actual goal is, the computer states you can find out in the Overseer's sealed orders but obviously you don't find them. In fact considering it's been, what, 3 generation or more since the bombs dropped? Chances are overseers are told about the experiment when the change is made, overseers are likely chosen for their loyalty to the current one.
Anyway, Exiled for:
Measured once, cut twice.
"Condiments were a privilege, not a right citizen. I'm afraid you'll have to go."
Exiled for failure to turn up to scheduled execution on time.
Teenaged hazing ritual gone awry, now you can't get back in.
Disagreeing with the teacher in physics class. "But radiation does work that way!"
Owning a goldfish without a license.