MathDB

A magician intends to perform the following trick. She announces a positive integer

n

, along with

2n

real numbers

x_1 < \dots < x_{2n}

, 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(x_1), \dots , P(x_{2n})

, 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?

Problem Statement