91st Analytic Beer

Abstract program:

1. Let A1, A2, ..., An be n points on the unit circle and assumpe that for all interior points P the product |A1P|...|AnP|<=2. Show that the n points are the vertices of the regular n-gon. (M.R.)
2. A player A thinks a polynomial with natural coefficients. The player B can ask about the value of the polynomial at an arbitrary real number. How many questions does the player B need to get all the coefficients? (A.N.)

Concrete program:

• Gambrinus 10^o, Radegast Birell
• filet with potatoes, chicken noodles with mustard sauce, "Porici Bang" with potato pancakes, toast with beer cheese, pancakes
• coffee

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