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Read full issue - Canadian Mathematical Society

THE ACADEMY CORNER No. 20 Bruce Shawyer 257 All communications about this column should be sent to Bruce Shawyer, Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada. A1C 5S7 THE BERNOULLI TRIALS 1998 The Bernoulli Trials, an undergraduate mathematics competition, was held Saturday, March 7 at the University of Waterloo. This is the second year for this event, which is a double knockout competition with \true" or \false" as the answers on each round. The participants have 10 minutes for each question, and drop out after their second incorrect answer. There were 29 student participants in the competition, which lasted 4 hours and 16 rounds. The winner was third year student Frederic Latour. Second place went to rst year student Joel Kamnitzer, and third and fourth to Richard Hoshino and Derek Kisman. In keeping with the nature ofthe answers required, the prizes were awarded in coins: 100 toonies for rst place, 100 loonies for second, and quarters for third and fourth. Ian Goulden and Christopher Small 1. In the gure below, the two circles are tangent at A. The point C is the center of the larger circle, and FC is perpendicular to AB. The line segment DB is of length 9, and the line segment FE is of length 5. A E F C D TRUE OR FALSE? The diameter of the larger circle is less than or equal to 49. B

- Page 2 and 3: 258 2. One of the participants in t
- Page 4 and 5: 260 15. Let A and B be two random p
- Page 6 and 7: 262 5. Let m be a positive integer.
- Page 8 and 9: 264 12 th Grade 1. Solve the equati
- Page 10 and 11: 266 , 6k + r 5 Now, 1 2 1 1 a + a +
- Page 12 and 13: 268 Then (1), (2) and (3) show that
- Page 14 and 15: 270 E F A B H C G Now BF = GF and \
- Page 16 and 17: 272 so that b c sin 1 sin 2 a b sin
- Page 18 and 19: 274 We have x 2 +(m 2 x,x1) 2 x(m 2
- Page 20 and 21: 276 Pythagoras Strikes Again! K.R.S
- Page 22 and 23: 278 m1; m2;m3 denote the medians ma
- Page 24 and 25: 280 side lengths are AD, DB; CD is
- Page 26 and 27: 282 J K A B E D L M (a) A (b) B (c)
- Page 28 and 29: 284 42 W 17. Which of the four tria
- Page 30 and 31: 286 MATHEMATICAL MAYHEM Mathematica
- Page 32 and 33: 288 there arenoterms of the form p
- Page 34 and 35: 290 (b) Deduce that if both q and t
- Page 36 and 37: 292 Since we have we have FH3 = DH1
- Page 38 and 39: 294 Theorem. Let A1A2A3A4A5 be a pe
- Page 40 and 41: 296 A Combinatorial Triad Cyrus Hsi
- Page 42 and 43: 298 Swedish Mathematics Olympiad 19
- Page 44 and 45: 300 J.I.R. McKnight Problems Contes
- Page 46 and 47: 302 1. p(t) p(t), 2. p(t) = p(t), 3
- Page 48 and 49: 304 2360. Proposed by K.R.S. Sastry
- Page 50 and 51: 306 B=2 =C=2 =xand A=2 = =2 , 2x. T
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308 220A ? .[1996: 363] Proposed by

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310 then ( ; ; k ) 2 @D0 " , and, b

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312 With r = p ab and x = log(a=r),

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314 Furthermore \OSI = \SOO 00 = (b

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316 2243. [1997: 243] Proposed by F

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318 Since f (0) = f (1) = f (2) = 0

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320 1X 1 The series k=1 k2 converge