There are two people, each has an integer which together multiply to $8$ or $16$,
A: I don’t know what number you have,
B: I don’t know what you have either
A: I still don’t know what number you have,
B: I still don’t know what number you have either
A: I know what you have now,
B: Oh mate, I still don’t know what you have
What’s the number that B has?
Best Answer
B has $4$.
The possible couples for $(A,B)$ are $(16,1),(1,16),(8,1),(1,8),(8,2),(2,8),(4,4),(4,2),(2,4)$.
First round you eliminate $(16,1)$ because $16$ is unique in A's side so he would have found.
Second one you remove $(1,16)$ and $(8,1)$ for the same reasons for B (taking into account the removed couples)
Then $(1,8)$ and $(8,2)$ for A
Then $(4,2)$ and $(2,8)$ for B
We're left with $(2,4)$ and $(4,4)$, B necessarily has $4$, A we dont know.