Something like happened to me once, someone asked me a riddle (it was: "you have a polynom of coefficients that are positive integers. I can give you the value

Something like happened to me once, someone asked me a riddle (it was: "you have a polynom of coefficients that are positive integers. I can give you the values of this polynom at integer points of your choice. Can you get all the coefficients by asking only two values?"). Somehow I got it very quickly, and was thinking in my head "oh man I didn't know I was that clever", but the guy thought I already knew the answer.