The Eighteenth Canadian Mathematical Olympiads
1986年第十八届加拿大数学奥林匹克 
 The triangle ABC has angle B = 90^{o}. The point D is taken on the ray AC, the other side of C from A, such that CD = AB. ∠CBD = 30^{o}. Find AC/CD.
 Three competitors A, B, C compete in a number of sporting events. In each event a points is awarded for a win, b points for second place and c points for third place. There are no ties. The final score was A 22, B 9, C 9. B won the 100 meters. How many events were there and who came second in the high jump ?
 A chord AB of constant length slides around the curved part of a semicircle. M is the midpoint of AB, and C is the foot of the perpendicular from A onto the diameter. Show that angle ACM does not change.
 Show that (1 + 2 + ... + n) divides (1^{k} + 2^{k} + ... + n^{k}) for k odd.
 The integer sequence a_{1}, a_{2}, a_{3}, ... is defined by a_{1} = 39, a_{2} = 45, a_{n+2} = a_{n+1}^{2}  a_{n}. Show that infinitely many terms of the sequence are divisible by 1986.

点击此处查看相关视频讲解 

