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Perplexing Polynomial Puzzle (Posted on 2005-06-13) Difficulty: 3 of 5
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?

See The Solution Submitted by Bractals    
Rating: 4.3333 (12 votes)

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Solution Perplexing! Comment 6 of 6 |

First, choose a=1. That will give you the sum of the coefficients. Then, choose a power of 10 that is greater than p(1) for b. That will give you the coefficients.

For example, suppose p(1)=7. Then, the sum of the coefficients is 7. Then, choose b=10. Suppose p(10)=232. Then, the polynomial is 2x^2+3x+2.


  Posted by Math Man on 2012-04-30 15:38:59
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