Question 18
A mysterious machine contains a secret combination consisting of 2016 integers $x_{1}, \ldots, x_{2016}$. We know that all combination numbers are equal except one. It is possible to query the machine by subjecting it a sequence of 2016 integers $y_{1}, \ldots, y_{2016}$. The machine responds by revealing the value of the $$
x_{1} y_{1}+\cdots+x_{2016} y_{2016} \text{.}
$$ sum after answering the first question, the machine accepts a second question, then a third, and so on. How many questions are needed to determine the combination:
(a) knowing that the different number is equal to zero?
(b) not knowing what the number is different?
x_{1} y_{1}+\cdots+x_{2016} y_{2016} \text{.}
$$ sum after answering the first question, the machine accepts a second question, then a third, and so on. How many questions are needed to determine the combination:
(a) knowing that the different number is equal to zero?
(b) not knowing what the number is different?