Problem #PRU-78244

Problems Algebra Absolute value Absolute value of a number (other) Algebra and arithmetic Number systems Decimal number system Algebraic equations and systems of equations Higher order equations. Palindromic polynomial equations Equations of higher order (other)

Problem

Two people play a game with the following rules: one of them guesses a set of integers \((x_1, x_2, \dots , x_n)\) which are single-valued digits and can be either positive or negative. The second person is allowed to ask what is the sum \(a_1x_1 + \dots + a_nx_n\), where \((a_1, \dots ,a_n)\) is any set. What is the smallest number of questions for which the guesser recognizes the intended set?