## Problem #023 - guess the polynomial

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In this problem you have to devise a strategy to beat the computer in a "guess the polynomial" game. ### Problem statement

I want you to play a little game with the computer. The computer is going to think of a polynomial with non-negative, integer coefficients. Let's say $$p(n)$$ is the secret polynomial the computer is thinking of.

I want you to find out what $$p(n)$$ is, and the only thing you can do is to ask for hints in the form of values of $$p(n)$$ for $$n \geq 0$$ integer. For example, you can ask what $$p(0)$$ or $$p(49)$$ is, but you can't ask for the value of $$p(-1)$$ or $$p(0.5)$$. You have to come up with the best strategy possible, that allows you to determine $$p(n)$$ with the least number of hints possible.

You can test your strategy with the computer below. The computer will only think of polynomials with degree at most $$3$$ and the coefficients will be at most $$3$$ as well, but that is just to make testing your strategy easier. The strategy should work for higher degrees and larger coefficients.

With the restrictions for the computer test, we have

$p(n) = c_0 + c_1n + c_2n^2 + c_3n^3, 0 \leq c_i \leq 3$

.

Your guess: p(n) =   +   n   +   n^2   +   n^3

If you need any clarification whatsoever, feel free to ask in the comment section below.