Problem of the Week 1098

Name that Tune ... er ... Polynomial!

Bob: Let's play "Name that Polynomial." I'm thinking of a polynomial p(x) with nonnegative integer coefficients. You need to guess what it is.

Alice: Is it bigger than a breadbox and smaller than a house?

Bob: Ha ha, very funny. If you give me any integer x then I will tell you the value of p(x).

Alice: You're not even going to tell me the degree of the polynomial?

Bob: Nope. Try to figure out p(x) using the fewest queries.

What is the least number of queries Alice needs to determine the polynomial p(x)? (Her first two questions above don't count!)

Source: Peter Winkler, Mathematical Mind Benders, A.K. Peters, 2008.

© Copyright 2008 Andrew Beveridge and Stan Wagon. Reproduced with permission.