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?

Given p(1), find any power of ten greater than p(1) --T=10^k>p(1)-- and ask for p(1/T). The desired coefficients will appear in the result.

With Eric's example (5x²+6x+2) we could have T=100, so we'd ask for p(0.01)=2.0605 and the coefficients are in plain sight. (T=1000 would ask for p(0.001)=2.006005)

Posted by Old Original Oskar! on 2005-06-13 21:55:47