Calvin and Peter each choose a positive integer and, without revealing it to the other, tell their choice to, say, Prof X. Suppose that Calvin chooses 2004 and Peter chooses 1019. Then Prof X writes the sum of the two chosen numbers on a blackboard, together with another integer he randomly chooses as he likes. Suppose the two numbers on the board are 3023 and 3203.
Calvin looks at the two numbers and announces to Peter that he does not know what Peter's number is. Peter looks at the two numbers and announces to Calvin that he does not know what Calvin's number is.
Calvin then announces to Peter that he still does not know Peter's number. Peter then announces to Calvin that he still does not know Calvin's number. And so on.
At some point, one of Calvin and Peter will be able to state what the other had chosen. Who will be the first to do so?
Details and assumptions: (I don't think I need to state this but still...for the sake of the problem) Assume that both, Calvin and Peter, are truthful and smart