Alice, Bob and Charlie play a game.
Alice writes down two positive integers on a blackboard visible to Bob and Charlie. She says that one of them is of her own choice, the other number is the sum of two positive integers, which were secretly communicated before by Bob and Charlie, respectively. Now Alice asks Bob, if he knows Charlies number. If he says "NO", the corresponding question goes to Charlie. If he says "NO", the question goes to Bob and so forth.

Can we expect a "Yes" answer at some point?

Alice, Bob and Charlie play a game.

Alice secretly communicates a positive integer to Bob, and a positive integer to Charlie.

Alice writes down two positive integers on a blackboard visible to Bob and Charlie.

She says that one of them is of her own choice, while the other is the sum of the two secret numbers.

Now Alice asks Bob if he knows Charlie's number. If he says "No", the corresponding question goes to Charlie. If he says "No", the question goes to Bob and so forth.

Can we expect a "Yes" answer at some point?