Alice: "I'm thinking of a polynomial f(x) with non-negative integer coefficients. Can you tell which one?"
Bob: "Well, I need some information."
Alice: "You can pick any real number r and I'll tell you f(r). Um....that is, I'll tell you finitely many digits of f(r) - but as many as you want."
Bob: "Gee - just one value of your polynomial? I dunno...."
Help Bob out. Tell him a good choice for r, and then how he can determine f(x) in finitely many steps.
The method of finding a polynomial using points on the polynomial is discussed in detail. The solution is detailed and well presented.