Arthur and Bert each writes down a positive integer on a piece of paper and then shows it to Charles. Charles then writes two numbers on a blackboard, visible to Arthur and Bert: one of them is the sum of Arthur's and Bert's numbers, and the other is a random number.
After this Charles asks Arthur if he knows Bert's number. If Arthur says he doesn't know, then he asks Bert if he knows Arthur's number. If Bert says he doesn't know, Charles continues with Arthur, then if necessary with Bert and so on... until he gets a positive answer.
When will Charles get a positive answer?
(In reply to
re(2): General formula by Tristan)
Tristan:
Now that we are using the same definitions, I think we do have a
difference. Consider A = B = 7, y = 14, x = 17. I think
that we get 5 no's before B answers yes. I think that your
formulas suggest 3 no's before B answers yes.
From my point of view,
The first no means A is between 1 to 13.
The 2nd no means B is between 4 to 13.
The 3rd no means A is between 4 and 10.
The 4th no means B is between 7 to 10.
The 5th no means A has exactly 7.
B answers y, I know what A has.
re(3): General formula
