Credit for this problem goes to MindYourDecisions. Thanks!

## Logicians Numbers

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?

Solution