2000 Advanced Topics #10: Figuring Each Other's Numbers
Source:
June 21, 2012
Problem Statement
I call two people and and think of a natural number . Then I give the number to and the number to . I tell them that they have both been given natural numbers, and further that they are consecutive natural numbers. However, I don't tell what 's number is and vice versa. I start by asing if he knows 's number. He says "no", Then I ask if he knows 's number, and he says "no" too. I go back to and ask, and so on. and can both hear each other's responses. Do I ever get a "yes" in response? If so, who responds first with "yes" and how many times does he say "no" before this? Assume that both and are very intelligent and logical. You may need to consider multiple cases.