Puzzle time - Recovering the Polynomial
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The Oracle at Delphi has in mind a certain polynomial p (in the variable x, say) of degree d with arbitrary real-valued coefficients. You may query the Oracle with any integer n>=0, and the Oracle will tell you the value of the n-th derivative of p at x = 3.1415927.
How many queries do you have to make to determine p?
Hint: Jolly already almost gave away the solution today.
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