Calvin and Peter are involved in a number guessing game. They each pick a positive integer at random and, without revealing it to the other, tell Prof X their choice. Prof X writes two numbers on a blackboard. One is the sum of the two numbers he gets from Calvin and Peter. The other number is chosen by Prof X at random.
Now Calvin looks at the two numbers and tells Peter that he doesn't know what Peter's number is. Peter looks at the two numbers and tells Calvin that he doesn't know what Calvin's number is.
Calvin again looks at the numbers and announces that he still doesn't know what Peter's number is. Peter looks at the numbers and says he too doesn't know that Calvin's number is. This goes on until one of them announces that he knows what number the other person had chosen. Who will be the first person to do so?
Details and assumptions: Assume Calvin's number is 1576, Peter's number is 2048 and Prof X has written 4000 and 3634 on the blackboard. Calvin and Peter are honest.