Polynomials/N/Guessing/Exercise

Two people, ${}A$ and ${}B$, play polynomial-guessing. In this game, ${}A$ imagines a polynomial ${}P(x)$, where all coefficients are in ${}\mathbb {N}$. Person ${}B$ is allowed to ask for the values ${}P(n_{1}),P(n_{2}),\ldots ,P(n_{r})$ for certain natural numbers ${}n_{1},n_{2},\ldots ,n_{r}$. Here, ${}B$ may choose these numbers arbitrarily, taking the previous answers into account. The goal is to find the polynomial.

Describe a strategy for ${}B$ to find always the polynomial, where the number of questions is (independent of the polynomial) bounded.

Create a solution