A magician intends to perform the following trick. She announces a positive integer n, along with 2n real numbers x1<⋯<x2n, to the audience. A member of the audience then secretly chooses a polynomial P(x) of degree n with real coefficients, computes the 2n values P(x1),…,P(x2n), and writes down these 2n values on the blackboard in non-decreasing order. After that the magician announces the secret polynomial to the audience. Can the magician find a strategy to perform such a trick? algebraIMO ShortlistIMO Shortlist 2020polynomialalgorithmlagrange s interpolationGerhard Woeginger