The 34th British Mathematical Olympiad
1998年第34届英国奥林匹克数学竞赛 
 A station issues 3800 tickets covering 200 destinations. Show that there are at least 6 destinations for which the number of tickets sold is the same. Show that this is not necessarily true for 7 .
 The triangle ABC has ∠A > ∠C. P lies inside the triangle so that ∠PAC = ∠C. Q is taken outside the triangle so that BQ parallel to AC and PQ is parallel to AB. R is taken on AC (on the same side of the line AP as C) so that ∠PRQ = ∠C. Show that the circles ABC and PQR touch .
 a, b, c are positive integers satisfying 1/a  1/b = 1/c and d is their greatest common divisor. Prove that abcd and d(b  a) are squares .
 Show that:
xy + yz + zx = 12
xyz  x  y  z = 2
have a unique solution in the positive reals. Show that there is a solution with x, y, z distinct reals.

点击此处查看相关视频讲解 

