43rd Eötvös Competition Problems 1939

1.  Show that (a + a')(c + c') ≥ (b + b')2 for all real numbers a, a', b, b', c, c' such that aa' > 0, ac ≥ b2, a'c' ≥ b'2. 2.  Find the highest power of 2 dividing 2n! 3.  ABC is