Here is the sixth Greenwich Maths Challenge. As usual there will be a small prize for the first correct solution emailed to A.Mann@gre.ac.uk by a Greenwich undergraduate.
If you specify the value of y at n different values of x there is a unique polynomial y=p(x) of degree n-1 which takes these values. But suppose I have a polynomial p(x) of unspecified degree, whose coefficients are all non-negative integers. If you give me a value of x I will tell you the value of p(x). What is the minimum number of evaluations you need to make, to be able to identify all the coefficients of my polynomial? To win the prize you must justify your answer.