[durron597]

Three perfect logicians are each given a number stuck to their forehead. They are told that all three numbers are distinct positive integers such that two of them add to the third.

Logician A looks at B and C and says "I do not know what my number is."

Logician B looks at A and C and says "I do not know what my number is."

Logician C looks at A and B and says "Then my number must be 50".

Logician A and B then both say, "Ah ha, my number must be _____", where "____" is different for the two logicians (obviously).

1) How did C figure out his number?
2) What are A and B's numbers?
3) How did they figure out their numbers?