Math League News (#2) 1/00

New Calculator Rule Our contests say that neither a TI-89 nor a TI-92 is permitted. That rule has changed. Since Contest 2, we have allowed any calculator without a QWERTY keyboard.

Contest Dates HS Contest dates are Nov. 30, Jan. 11, Feb. 8, Mar. 7, and Apr. 11. A registration form for our April Algebra Course I Contest is enclosed. Do you have a schedule conflict with our contest dates? Our rules say that, in case of vacations, special testing days, or other disruptions of the normal school day, you may give the contest on an earlier day-but you must still mail scores by Friday of the official contest week. If scores are late for due cause, please attach a brief explanation. We reserve the right to consider as unofficial late scores lacking such an explanation.

Regional Groupings We sometimes receive requests about regional groupings. Within guidelines, we try, when possible, to honor such requests for the next school year.

Student Cumulative Scores Completion of the Cumulative Column is optional, but we list (and consider official) only cumulative scores reported in this column. A student whose cumulative scores are incorrect (or which don't appear regularly in the Cumulative Column) may lose eligibility for recognition by the League.

What Do We Print in the Newsletter? Our policy is to print every solution and comment we receive, newsletter space permitting. But we prepare the newsletter before the score report, so slow mail (a big problem in December!) means we don't print some comments. Finally, we may say "so-and-so sent an alternate solution" when tight space means we don't have room to print it.

Some Tips on Getting Students Involved One advisor asked how to persuade more "always busy" students to take our half-hour contests. Would you like to share your tip? Here's a start: 1) Hold contests during lunch. Serve ice cream or fruit to those who eat while writing the contest. 2) Use a bulletin board to name top students on each grade. Make a loudspeaker announcement too. 3) Send a report to a local community newspaper. 4) Serve cookies and drinks, with funds provided by the student government. 5) Hold the contest jointly with a neighboring school. The kids will enjoy the occasional travel and meeting kids from another school. 6) Post a colorful announcement the day before the contest so no one "forgets" about it on the day of the contest. 7) At Awards Night, give our Certificate to the students on each grade level who score highest on the contests.

Scanning Our (Copyrighted) Solutions One high school senior asked for permission to email scanned copies of our (copyrighted) contest solutions to others on his school's math team, which met monthly. We granted permission for that use.

General Comments About Contest #2 John Benson wrote to "complement you on contest 2. You had two simple problems (2-1 & 2-3) that could easily lead to carelessness. You had two "nice" algebra manipulation problems (2-2 & 2-4)-most manipulations aren't nice-a wonderful square, vector, slope problem (2-5), and a marvelous logic, number sense, counting problem (2-6). It was an absolutely delightful contest. You made my day." John also wrote that he was impressed that my son had proven a famous theorem. (He proved the Taniyama-Shimura Conjecture, a result connected to Wiles' proof of Fermat's Last Theorem.) Joe Holbrook made the interesting observation that his younger students did better than the older ones on 2-5 and 2-6. Dave Farber said "this was another interesting contest." Liz Martzuk said "Great questions." M. Dewey called contest 2 "fun to the (n!)th degree." Brian Balsdon said his "grade 9's had a chance at every question, so they were not at all discouraged." He joked that "2-3 was a little `cheesy.'" John Cirillo echoed that sentiment. "My students needed this contest. They were intimidated by contest #1. Contest #2 was exactly what the doctor ordered. The kids need a confidence boost every now and then." One advisor wrote to advise us that problem 2-2 ("except for the remainder") was the same as a problem in Kaplan's 1999 SAT Prep Book. We're not concerned if different people write similar problems occasionally.

Problem 2-1: A Partially Denied Appeal Two advisors asked if they should award credit for "a = 1, b = 2" instead of giving the answer as the ordered pair (1,2), as asked for in the question. Our rule does not allow credit if a specific form has been requested and the answer is not given in the required form.

Problem 2-2: Alternate Solutions Kevin Mosley cleverly noted that, when the remainder upon division by 7 is 5, the remainder fraction is 5/7. Double to get 10/7, or 1 3/7. Hence, he remainder after doubling is 3. Dave Farber used moduli.

Problem 2-3: Comments John Quintrell said "Problem 2-3 has us all a bit confused. I looked at it as a typical "work" problem, but it was actually even easier if you read it carefully. I figured!" Halyna Kopach "did not like question 2-3. I felt this was a reading problem more than a math problem."

Problem 2-4: Comments, Alt Sol, Denied Appeal An appeal involving a = -1 or b = -1 was denied since such values make the given equation invalid. The ruling was made by Prof. Brian Conrad, Harvard Univ. Math. Dept. Dave Farber and Dave Stouffer sent in solutions obtained by different algebraic techniques. This problem offers an amazing range of solutions. Dick Olson said his students missed this but "were beside themselves when they saw how simple it was to multiply by (a+1)(b+1)."

Problem 2-5: Alternate Solution Dave Stouffer used slopes and the distance formula (setting sides of the square equal in length) to compute the x- and y- intercepts, from which he could determine (x,y). Dave Farber also sent an alternate solution.

Problem 2-6: Comments and Appeals Dick Olson called 2-6 "a gem." Keith Calkins said that "the wording on 2-6 was tough-keeping the digits in order was implicit in the word delete." The other 500 billion people who wrote to us wanted us to leave 5 8s and 6 9s and rearrange them to get 99999988888, or multiply them to get 17414258690000000000. That's the whole point!! The directions did not say "delete and rearrange." They did say "Call the resulting number n." The value of n that "results" depends solely on selecting which digits to delete. These appeals were denied by Prof. B. Conrad, Math Dept., Harvard Univ.

Statistics / Contest #2

Prob #, % Correct (top 5 each school)

2-1    96%2-4    43%
2-2    98%2-5    71%
2-3    98%2-6    20%