Two mathematicians are passing an exam, where the examiner informs them that he has chosen two different numbers between 2 and 100, such that one is divisible by the other. The examiner then tells the sum to the first mathematician A and the difference to the second mathematician B, in such a way that none knows which number has been whispered to other.
The two mathematicians start this discussion:
- A: I don't know the numbers.
- B: I already knew this.
- A: I already knew that you knew this.
- B: I already knew that you knew that I knew that you didn't know.
- A: I still can't figure out what the two numbers are.
- B: Oops, I think I miscalculated my last statement!!! As a matter of fact, I didn't know this already!!!
Question: What are these two numbers again??
For hints and notes, refer to the following links:
Deducing Two Numbers based on their Difference and Ratio
What are the numbers?