3rd Australian Mathematical Olympiad Problems 1982

A1.  If you toss a fair coin n+1 times and I toss it n times, what is the probability that you get more heads? A2.  Show that the fractional part of (2 + √3)n tends to 1. A3.  In the triangle ABC, let the angle bisectors of A, B, C meet the circumcircle again at X, Y, Z. Show that AX + BY + CZ is greater than the perimeter of ABC. B1.  For what d