Guess the Polynomial

Question

Player ONE has a finite degree polynomial $p$ with integer coefficients in mind whose domain is the reals.

Player TWO gets to ask Player ONE to evaluate the polynomial at two points $x_0,x_1$ and Player ONE responds with $p(x_0)=y_0$, and $p(x_1)=y_1$.

With this information, can Player TWO guess the polynomial?

I have figured out the solution to this problem, but I wanted to post the problem on SE so that you guys could have fun with it. Cheers!

Related: http://math.stackexchange.com/questions/446130 – Watson Jun 07 '16 at 11:30 — Watson, Jun 07 '16 at 11:30

score 5 · Answer 1 · answered Nov 13 '13 at 22:42

5

Ask for $x_0=\pi$ and ignore your second chance.

answered Nov 13 '13 at 22:42

Hagen von Eitzen

Yep. heheheheheh. Now if we ask that both $x_0, x_1$ cannot be transcendental ? – Rustyn Nov 13 '13 at 22:45
@Rustyn If $x_0,x_1$ must be algebraic, let $f,g\in\mathbb Z[X]$ be polynomials with $f(x_0)=g(x_1)=0$. Then we player two cannot tell apart $p$ from $p+fg$ ... – Hagen von Eitzen Nov 13 '13 at 23:02
Could you please explain your answer? – Martin Thoma Nov 18 '13 at 16:46

1 Answers1