18th International Mathematical Olympiad 1976 Problems & Solutions

A1.  A plane convex quadrilateral has area 32, and the sum of two opposite sides and a diagonal is 16. Determine all possible lengths for the other diagonal. A2.  Let P1(x) = x2 - 2, and Pi+1 = P1(Pi(x)) for i = 1, 2, 3, ... . Show that the roots of Pn(x) = x are real and distinct for all n. A3.  A rectangular box can be completely filled with unit cubes. If one

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