Do you Know the Answer to this Math Puzzle?
Question:Eight hockey teams are playing in a tournament. A computer randomly assigns teams to play one another. Every game is played until one of the two teams wins, so games never end in a draw. As soon as a team loses three games it is knocked out of the tournament and the last team remaining wins the tournament. Find the smallest number and the largest number of total games that could be played in the tournament. |
Answer:Every time a game is played one team loses so the total number of games is exactly the same as the total number of losses. Seven of the teams lose exactly 3 games each while the winning team loses 0, 1 or 2 games. Therefore the smallest number of games that could be played is 7 x 3 + 0 = 21 and the largest number of games is 7 x 3 + 2 = 23. If the computer always pairs the ultimate winner against some other team it’s easy to create scenarios where exactly 21 games and exactly 23 games are played. |
David Bigelow, Ph.D. Island Times Magazine would like to welcome Dr. David Bigelow to our monthly features. Thank you, Dave, for your support.
David Bigelow, Ph.D. is Chair of the Department of Mathematics at Vancouver Island University. Dr. Bigelow has been witness to many developments over the nineteen years of his employment at VIU. In 1990, VIU was the fledgling “Malaspina University College.” At that time, the Department of Mathematics offered a university transfer program in mathematics, with only first and second year courses. Now, VIU offers a Minor in Mathematics, with plans of developing a Major due to ever-increasing interest from students. For any students who might be intimidated by math, VIU is one of few universities that offer free tutoring in the Math Learning Center, by upper-level students. Dr. Bigelow earned his Master’s degree and Ph.D. in Mathematics from the University of Waterloo, in Ontario. When asked how his interest in math began, Bigelow responded, “It was a process, rather than a moment,” as he sat back, fondly remembering a story about his father, who was a biochemist. Bigelow’s first interest was in astronomy. One night while sitting with his father, the then eight-year-old Bigelow questioned the theory of a universe filled with infinite space. He was convinced that at some point, if travelling in a spaceship, one would certainly hit a brick wall. To this reasoning, Bigelow’s father responded, “Okay, then what would be behind the brick wall?” “Well, more space,” Bigelow replied. Years later, curiosity about mathematics finally led Bigelow to a linear algebra course while attending the University of Manitoba. It was this course that cemented his future in mathematics. Bigelow knew that he had found his calling. So, what is math according to Dr. Bigelow? “If I had to describe math in only a few words, I would say that math is about measuring and counting. How would you describe things such as speed, height, weight, density, and temperature without math? The list goes on and on. Many everyday processes involve math,” said Bigelow.
Dr. Bigelow is a well-respected member of Vancouver Island University’s faculty, known for his entertaining, and somewhat theatrical method of inspiring students to go from fearing math, to enjoying it; frequently Bigelow’s calculus students smile and giggle, mostly at Bigelow’s expense. Bigelow enjoys being the catalyst of the transformation of calculus fear into appreciation, and creating a “fired-up” attitude in his students.
Outside of VIU, Bigelow also enjoys golf, cooking, and Scrabble, and has won the annual Scrabble tournament hosted by Literacy Central Vancouver Island three times in the experienced division. One day, if you have the privilege of becoming acquainted with Dr. David Bigelow, ask him about the yellow banana suit. |
