-----Original Message----- From: math-fun-bounces+cordwell=sandia.gov@mailman.xmission.com [mailto:math-fun-bounces+cordwell=sandia.gov@mailman.xmission.com]On Behalf Of Gary McGuire Sent: Wednesday, March 08, 2006 5:24 AM To: math-fun Subject: Re: [math-fun] sudoku, uniqueness, proofs Michael Kleber wrote: [deleted part] Dan wrote:
Are you sure that such solutions *are* given full credit in Putnam exams and Olympiads? I don't know if that's the case.
No, I'm not sure. I thought there would be some readers of this group who know. I know this particular problem is easy to solve the other way, but I've seen tricky problems which are made much easier by reasoning "here I am sitting in a Putnam/whatever, therefore this problem has a nice solution, therefore....." [deleted part] Gary McGuire _______________________________________________ I coach a MathCounts (grades 6-8) team, as well as high school students preparing for various contests. On many of the lower-level contests (say, MathCounts or the AMC->12 and the AIME), the exam only asks for the answer. In this case, I think that noticing, say, that a problem doesn't seem to have enough information, and fixing an apparently arbitrary value that will allow one to easily solve the problem (within the logical constraints) falls under a mixture of math and test-taking skills. For the AMC->12, many of the kids are, in ability, close to making the cutoff (a score of 100) for qualifying for the American Invitational (AIME), so I also have them work out the strategy for how many questions they should answer in certain situations. The AMC scores the 25-question exam by giving 6 points for each correct answer (multiple choice), 2.5 points for each unanswered problem, and 0 for each incorrect problem. If one's goal is to attain a score of >= 100, then, there's no advantage in answering 12 questions vs. 11 questions (and a possible disadvantage), but one needs to answer at least 11 questions. Qualifying for the AIME is not a zero-sum game, so I think that it is reasonable to point out this strategy to the kids. By the time that they reach the USAMO, they will be writing proofs for the problems; I've not graded those exams, but I would be surprised if a student got full credit for assuming that a solution was unique as part of his proof, unless he could show it later. Philosophically, I admit to being bothered when, say, a basketball team is in the lead and it intentionally delays, to deny the other team a chance at winning. I understand that this is within the rules, but it bugs me. I don't see the above strategies in that light, as one is not denying his competitors the same chance. However, I would not categorize using the strategies as "being better at math". --Bill Cordwell