Consider the following game: Alice chooses a polynomial p with non-negative integer coefficients and challenges Bob to determine the polynomial. Bob is allowed to ask Alice for the value of p(n) for an n of his choice and upon receiving the answer can ask Alice for the value of p(m) for an m of his choice. Is there a strategy for Bob such that after receiving these two values he can always determine the coefficients of Alice’s polynomial?
On first glance, this looks pretty tough for Bob: Alice has infinitely many choices, and isn’t even constrained in the degree of the polynomial she chooeses. However, there’s a really easy winning strategy for him: first ask for p(1) and then ask for p(m) for any m greater than p(1). That’s it!