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A program that learns your polynomial using just two queries

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Guess your polynomial

Secretly pick a polynomial in one variable with nonnegative integer coefficients. Then answer just two questions and watch as your polynomial is read back to you! It's not magic, it's maths.

$ python guess.py  
What is f(1)? 4
What is f(5)? 56
Your polynomial is: 

	1 + 1 x^1 + 2 x^2

Explanation

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A program that learns your polynomial using just two queries

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