Lynn's class held a checkers tournament. They had several rounds. Each person played one game per round until they lost. Lisawas the winner becasue she beat Matt in the last round. Only 24 students participated, because several were absent. Afterward, I asked Lynn how many games had been played. How would you answer?
Try smaller problems and look for patterns.
Make up names, make lists.
The first round had 12 games, the second round had 6, the third 3, the fourth 1, and the fifth 1, for a total of 23.
Possible difficulty: Why 1 in the fourth? Respond: idea of a bye.
Each person except the ultimate winner must lose one game, so the number of games will be one less than the number of playersthat is, 23.
Respond: Some solutions seem more elegant that others. Why? What is elegance in mathematics? Brevity? Generalizability? Insightfulness?
Prepare to teach this problem by working with a group of virtual students.
Have you used this problem with a class and seen approaches other than(or more specific than) those mentioned above? Or do you have other comments or criticisms or stories? If so, please tell us!
Last updated 30 November, 2004