Two logicians (A and B) each pick a whole number from 1 to 30 inclusive. The following conversation happens:
A: “Is your number double mine?”
B: “I don’t know. Is your number double mine?”
A: “I don’t know. Is your number half mine?”
B: “I don’t know. Is your number half mine?”
A: “I don’t know.”
B: “I know your number.”
All the statements are true. What is A’s number and how did B know?
