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The 29th Canadian Mathematical Olympiads
1997年第二十九届加拿大数学奥林匹克
  1. How many pairs of positive integers have greatest common divisor 5! and least common multiple 50! ?
  2. A finite number of closed intervals of length 1 cover the interval [0, 50]. Show that we can find a subset of at least 25 intervals with every pair disjoint .
  3. Show that 1/44 > (1/2)(3/4)(5/6) ... (1997/1998) > 1/1999 .
  4. Two opposite sides of a parallelogram subtend supplementary angles at a point inside the parallelogram. Show that the line joining the point to a vertex subtends equal angles at the two adjacent vertices .
  5. Find ∑0≤k≤n (-1)k nCk /(k3 + 9k2 + 26k + 24), where nCk is the binomial coefficient n!/( k! (n-k)! ).
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