MathDB

A mysterious machine contains a secret combination of

2016

integer numbers

x_1,x_2,\ldots,x_{2016}

. It is known that all the numbers in the combination are equal but one. One may ask questions to the machine by giving to it a sequence of

2016

integer numbers

y_1,\ldots,y_{2016}

, and the machine answers by telling the value of the sum

x_1y_1+\dots+x_{2016}y_{2016}.

After answering the first question, the machine accepts a second question and then a third one, and so on.
Determine how many questions are necessary to determine the combination: (a) knowing that the number which is different from the others is equal to zero; (b) not knowing what the number different from the others is.

Problem Statement