TIFR CSE 2024 | Part A | Question: 15

Question

Suppose Michelle gives Asna and Badri two different numbers from $\mathbb{N}=\{1,2,3, \ldots\}$. It is commonly known to both Asna and Badri that they each know only their own number and that it is different from the other one. The following conversation ensues.

Michelle: I privately gave each of you a different natural number. Which of you has the larger of the two numbers?

Asna: I don't know.
Badri: I don't know either.
Asna: Oh, then I know who has the larger number.
Badri: In that case, I know both numbers. What numbers were Asna and Badri respectively given?

• A. Asna was given $2$, Badri was given $3$.
• B. Asna was given $3$, Badri was given $2$.
• C. Asna was given $3$, Badri was given $4$.
• D. Asna was given $4$, Badri was given $3$.
• E. None of the above.

   

Answer 1

• Asna I don't know. So Asna does not have 1

• Badri I don't know either. So Badri does not have  or  1 Or 2

• Asna   I know who has the larger number. So Bob has  2 Or 3 

• Badri In that case, I know both numbers. If Asna knows which Badri  has then she has the other, and (from earlier) she does not have  3

So Asna  has 2  and Bob has 3