IMO 2020 Shortlist A5
A magician intends to perform the following trick. She announces a positive integer n, along with 2n real numbers x1 ă ....
Category: Algebra
Problem
A magician intends to perform the following trick. She announces a positive integer n, along with 2n real numbers x1 ă ... ă x2n, to the audience. A member of the audience then secretly chooses a polynomial Ppxq of degree n with real coefficients, computes the 2n values Ppx1q,...,Ppx2nq, 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? (Luxembourg)