MathDB

Alice and Bob play the following number-guessing game. Alice writes down a list of positive integers

x_{1}

\cdots

x_{n}

, but does not reveal them to Bob, who will try to determine the numbers by asking Alice questions. Bob chooses a list of positive integers

a_{1}

\cdots

a_{n}

and asks Alice to tell him the value of

a_{1}x_{1}+\cdots+a_{n}x_{n}

. Then Bob chooses another list of positive integers

b_{1}

\cdots

b_{n}

and asks Alice for

b_{1}x_{1}+\cdots+b_{n}x_{n}

. Play continues in this way until Bob is able to determine Alice's numbers. How many rounds will Bob need in order to determine Alice's numbers?

32