1. Suppose a cylindrical can C is inscribed in a unit cube so its axis lies along the main diagonal of the cube. Its radius can be anywhere between 0 (vol(C) = 0) and the radius of the circle inscribed in the hexagonal cross-section of the cube (vol(C) = 0). QUESTION: What radius maximizes the can's volume? 2. Let Z+ be the positive integers and let a > 0 be an irrational real. Define F: Z+ --> Z+ via F(n) = #( [n,n+1) int { K + L*a : K,L are in Z+} ). QUESTION: Find an asymptotic expression for F(n) as n --> oo. --Dan A.