[math-fun] Guess my numbers

This may be an old chestnut, but I only encountered it once (and that was almost forty years ago), so I'd appreciate references. Suppose I've picked n positive integers x_1, x_2, ..., x_n, which it's your job to guess. Each of your questions must be of the form "What is the value of a_1 x_1 + a_2 x_2 + ... + a_n x_n?", where a_1, a_2, a_3, ... are positive integers you get to choose. How many questions must you ask me to be assured of being able to deduce my n numbers? I got this wrong when I first heard it. Hint: The answer isn't n. Please, no spoilers till Thursday; but any leads that don't include spoilers are welcome right away! Thanks, Jim