Ask an opponent to choose a polynomial p(x) with nonnegative integer coefficients (of any degree). Tell him you can determine what it is (degree and coefficients) with just two values: you choose a and ask for p(a), then choose b and ask for p(b). What is a winning strategy?

The restrictions placed on this make it rather easy.

First, start with 1. This will give you the total sum of the coefficients, which must be greater than or equal to some number n for an n-degree polynomial.

Then, you can ask for any number b greater than the total sum of the coefficients. When you get this answer, you need to convert it to the base b and that will give you the coefficients.

For example, if you have 5x² + 6x + 2, giving 1 will get you an answer of 13. Suppose you then ask for 15. Your answer will be 1217. Converting this to base 15 will give you 562.

Posted by Eric on 2005-06-13 20:59:50