beero1000
Veteran Member
Was thinking about this brain teaser today:
I have a polynomial p(x) with non-negative integer coefficients. If you give me an integer n, I will tell you the value of p. Find an approach that uses the optimal number of queries in order to completely determine my polynomial. How many queries does it take?
I think I posted this here already (at some point and in some incarnation of the board). It's still a good one if you haven't seen it, or don't remember. The answer is much lower than might seem possible initially (it might actually initially seem impossible ). Anyway, got to thinking about the multivariate case, which I don't think I'd really considered before:
I have a polynomial p(x1,x2,...,xm) with non-negative integer coefficients. If you give me integers n1,n2,...,nm, I will tell you the value of p(n1,n2,...,nm). Find an approach that uses the optimal number of queries in order to completely determine my polynomial. How many queries does it take?
Think I can answer this one too. It's still really low.
I have a polynomial p(x) with non-negative integer coefficients. If you give me an integer n, I will tell you the value of p. Find an approach that uses the optimal number of queries in order to completely determine my polynomial. How many queries does it take?
I think I posted this here already (at some point and in some incarnation of the board). It's still a good one if you haven't seen it, or don't remember. The answer is much lower than might seem possible initially (it might actually initially seem impossible ). Anyway, got to thinking about the multivariate case, which I don't think I'd really considered before:
I have a polynomial p(x1,x2,...,xm) with non-negative integer coefficients. If you give me integers n1,n2,...,nm, I will tell you the value of p(n1,n2,...,nm). Find an approach that uses the optimal number of queries in order to completely determine my polynomial. How many queries does it take?
Think I can answer this one too. It's still really low.