Math League News (#3) 1/99

Which Calculators Are NOT Allowed? Our contests do not permit the TI-89 or any calculator with a QWERTY keyboard, such as the TI-92.

Future Contests and Rescheduling Contests Contest dates are Feb. 2, Mar. 9, and Apr. 13. Our annual Algebra Course I Contest is in April. If circumstances (such as school closings or special testing days) require it, we permit you to give the contest on another date. If your scores are late, please attach a brief explanation, or the scores may be considered unofficial.

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

T-Shirts Anyone? We're often asked "Are T-shirts available? The logo lets us know fellow competitors." Featuring grey shirting and a small, dark blue logo in the "alligator region," MATH T-shirts are available in all sizes at a very low price. There's just one low shipping charge per order, regardless of order size. For a VISA or MasterCard order, please phone 1-201-628-6328. You may fax a purchase order to 1-201-816-0125.

General Comments: Dave Mecham said "Every problem was solved by at least 1 student, a great morale booster. Sometimes, students get the idea that only super brains can solve some of the problems." Patrick Farrell and Nancy Looker both "love the contests as they are-don't go to group solutions." Patrick added "We'd prefer no contests in January." Wayne Akey, David Abineri, Father Mannin, and Elmer Delventhal called it a "Great contest!" D. Stoufer's "kids were thrilled with the results." Mike Buonviri thought contest 3 was "easier that the first two. Start the year off with one like this, and more students may be encouraged to participate." We agree. We usually get it right, but not this time! Suzanne Moll said "The student's loved it." Duane Bollenbacher said "Your problems are truly `problem-solving' problems, and yet they completely connect with the mathematics curriculum." Donald Cameron said it was "A good contest to attack immediately upon return from Christmas-easier than most, yielding higher scores, and giving good encouragement to all." Dwayne Cameron said "I don't remember our team score ever being this high." T. Butler asked "Were the first 3 all Pythagorean Theorem for a particular reason?" No reason except "Oops"!

Alternate Solution to Problem 3-1 Mark Snyder placed the diagram on graph paper and used the distance formula.

Problem 3-3: Comments and an Appeal (accepted) Brent Ferguson is "glad you include problems which require careful and correct interpretation." Wayne Akey thought the problem "was somewhat confusing." One appeal for "the length of the segment that makes a right angle with the chord" was accepted, but reluctantly. The problem itself fixed the center as one endpoint.

Problem 3-5: Comments, Alt Sol, an Appeal (denied) An appeal for (0, 3, ¥) was denied, since ¥ is not an integer. Wayne Akey, Dwayne Cameron, and Laurent Cash said that, with the table feature of the TI-82 or 83, "one can see the solution in seconds." Cash called it "electronic guess and check." Lorraine Diekemper said that x-2, x-4, and x-6 are factors of x, so she set x = (x-2)(x-4)(x-6) and got x = 3. Bob Smith's students used educated trial and error. Bryan Knight said "The solution to 3-5 assumed that x is an integer" and asked for a proof. We should have said x was an integer. Send us a SASE, and we'll send you Prof. Conrad's two-page proof that x must be an integer in problem 3-5.

Problem 3-6: Comments & An Appeal (denied) Appeals claiming that "no loss of time" referred to the entire sequence of Pat turning, rowing downstream, and retrieving the hat were denied by our appeals judge, Harvard math professor Brian Conrad. The appeals contradict the problem's words that say "If the river flows at a constant rate, and Pat rows at a constant rate (relative to the river) . . . , what is the river's rate, in km/hr?" Since Pat rows at a constant rate (relative to the river), Pat can't do all three things in 0 time. Student Jason VanBatavia found a guess & check solution. Dave Farber and Dwayne Cameron said "3-6 sounded like a classic Algebra 2 problem from the 1960's." Farber sent a 3 equation, 4 variable solution. Bryan Knight said "3-6 was especially interesting." Bob Smith said "I wrote equations forever, but got nowhere. Your train analogy is excellent. Note that the basis for the solution (10 minutes to return for the hat) is invariant, even in calm water. Thanks for another great exercise." Jerry Detweiler said most math books would discuss the boat's rate in still water instead of the constant rate, relative to the water. "What I like about the League is that it gives me new ways to look at things. One of our teachers never thought that if you row upstream for 10 minutes, then downstream for 10 minutes (at a constant rate), you end up at the same spot on the river." Elmer Delventhal objected, "as a former engineer," to accepting 3 as an answer. The question asked for "the river's rate, in km/hr," so the units were stipulated. Brian Baledan liked 3-6 because he once had a "student who found a solution like your `train' solution when he `just stopped the river.'" Mike Buonviri said "The train analogy helped us visualize the concept."

Statistics / Contest #4

Problem #, % Correct (top 5 each school)

3-1    96%3-4    71%
3-2    90%3-5    75%
3-3    74%3-6    33%