Question 96
Anana has an ordered $n$-tuple $(a_1, a_2, ..., a_n)$ of integers. Banana may make a guess on Anana's ordered integer $n$-tuple $(x_1, x_2, ..., x_n)$, upon which Anana will reveal the product of differences $(a_1 - x_1)(a_2 - x_2)...(a_n - x_n)$. How many guesses does Banana need to figure out Anana's $n$-tuple for certain?