Question 10
A teacher chooses integers $m,n$ with $2\le m\le n$. She tells Peter only $mn$ and Steven only $m+n$. They have the following conversation:
Peter: I cannot deduce the sum.
Steven: Knowing that, I still cannot deduce the product.
Peter: Knowing that, I still cannot deduce the sum.
Steven: Now I can deduce the product. Assuming both are perfect logicians, find $n-m$.
Peter: I cannot deduce the sum.
Steven: Knowing that, I still cannot deduce the product.
Peter: Knowing that, I still cannot deduce the sum.
Steven: Now I can deduce the product. Assuming both are perfect logicians, find $n-m$.