You invite two perfect logicians, Alf and Bertie, to play a game. Each of them is given a positive integer (i.e., one of 1, 2, 3, etc.) They’re also told that the other one’s number differs by exactly one from his; that is, if Alf has 3, he knows that Bertie has 2 or 4. They’re then asked alternately if they know what the other one’s number is:
A few questions for you:
1. What is Alf’s number?
2. What is Bertie’s number?
3. In general, if the Nth answer is the first “Yes”, what are Alf and Bertie’s numbers respectively?
rot13 any answers, so people can keep playing. (This means that you should spell out any numbers, since the rot13 of “42” is “42”.)