42nd Polish Mathematical Olympiad Problems 1991

42nd Polish Mathematical Olympiad Problems 1991A1.  Do there exist tetrahedra T1, T2 such that (1) vol T1 > vol T2, and (2) every face of T2 has larger area than any face of T1? A2.  Let F(n) be the number of paths P0, P1, ... , Pn of length n that go from P0 = (0,0) to a lattice point Pn on the line y = 0, such that each Pi is a lattice point and

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