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?

First, choose a=1. That will give you the sum of the coefficients. Then, choose a power of 10 that is greater than p(1) for b. That will give you the coefficients.

For example, suppose p(1)=7. Then, the sum of the coefficients is 7. Then, choose b=10. Suppose p(10)=232. Then, the polynomial is 2x^2+3x+2.

 

Posted by Math Man on 2012-04-30 15:38:59