Math League News (#1) 11/99

New Calculator Rule Our contests say that neither a TI-89 nor a TI-92 is permitted. We changed that rule. Starting with Contest 2, we allow 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.

Received Your HS Contest Package Late? If you have not yet received the contests, phone 1-201-568­6328 so we can ship another set. If you just recently got the contests, please take Contest #1 as soon as possible, even if it's late!

The Score Report and the Cumulative Column Students on your score report must take the contest at the exact same time. Do not include students taking the contest during any later class period. Below is part of a score report. The Total column is for Contest 2 totals only. The Indiv. Cumulative is for student totals for the first 2 contests. This column is optional; but high scoring students not tallied here cannot be named in our newsletter. Chris Lewis got 5's on the first 2 contests and had a cumulative total of 10. Pat Harris got a 5 and had a cumulative total of 9. Team members may vary each contest-use your school's 5 best scores each time, and submit additional sheets if needed. Be sure to check the "Contest Number" box, and enter your Team Score at the top of the form.

Highest Scoring Participants
Please PRINT
Last Name, First Name
Question
 
 
1
2
3
4
5
6
Total
Indiv. 
Cumulative
1. Lewis, Chris
1
1
1
1
1
0
5
10
2. Harris, Pat
1
1
1
1
1
0
5
9
3. Smith, Lee
1
1
1
0
0
0
3
 
4. Nelson, Jan
1
0
1
1
0
0
3
 
5. Sun, Ronnie
1
1
0
0
0
0
2
 
TEAM TOTALS
5
4
4
3
2
0
18
 

Completion of the "Cumulative" column is optional, but must be completed for any student who might be listed as a League high scorer.

Authentication of Scores To give credibility to our results, we authenticate scores high enough to win recognition. Awards indicate compliance with our rules. Please ask students to read the Selected Math League Rules on the back of this newsletter and sign a sheet to confirm knowledge of the rules. Keep the signed copies. Do not send them to us unless we request authentication from you.

General Comments About the Contest Marlene Dewey called it "a gr8 contest with 1derfully inviting questions 4 all 2 enjoy." S. Wong wrote "we found this contest to be very challenging, in fact one of our lowest team scores ever. The difficulty level may discourage students from returning." Daren Starnes called it "a very good first contest-q nice mix of numerical, geometric, and algebraic - some real thought provokers." One school wrote that they were giving proficiency tests. Our rules allow you to reschedule a contest when there are "special testing days." Student Daniel LeCheminant wrote "The Math League is great. I enjoy the problems where I can put all of my knowledge to work. Thanks for a wonderful program."

Problem 1-1: Appeal (Denied) Three appeals asked us to accept 0.09 as the answer instead of 9. The claim was that a number like 0.54 is a two-digit number. Our appeals judge, Prof. Brian Conrad, Harvard University Math Dept., denied the appeals. Prof. Conrad said that "a two-digit number must be an integer."

Problem 1-2: Comments An unknown correspondent wrote "1-2 was a GREAT stop-and-think-a-minute problem. It let students know they don't always need to reach for a calculator." M. Dewey thought "#1-2 was simple, yet cleverly designed-the students had to read the question carefully." Daren Starnes called 1-2 "a nice illustration of what the Pythagorean Theorem means."

Problem 1-3: Comments Daren Starnes said "many of my students missed 1-3 because they do not enumerate cases in many situations any more." Our unknown correspondent said 1-3 "was not a good problem for this type of test. It was too lengthy a process to write out all the possibilities."

Problem 1-4: Alternate Solution and Comment Bob Smith said that, since 640x = 26(10x) = 10y implies that x = 56, since each value of 2 must be multiplied by 5 to get a power of 10. Daren Starnes said "1-4 surprisingly stumped many students even though an easy calculator procedure was available to help."

Problem 1-5: Comments, Appeals (Denied), Alternate Solution Jeanne Kerk called 1-4 "a good, fun problem." One student asked us to accept his answer of "42 - b2 - g2" as correct. The appeal was denied by Prof. Brian Conrad of Harvard Univ. You simply cannot give the "value" of something in terms of itself. Bryan Knight and Mike Buoviri independently sent the same beautiful alternate solution which avoids the trial and error needed in our official solution. Since b2 + b + g2 + g = b(b + 1) + g(g + 1) = 42. we can just list a few products of consecutive integers and find the two whose sum is 42. Indeed, 3 4 + 5 6 = 42. An unknown solver sent another solution based on an interesting factoring.

Problem 1-6: Alternate Solution Student Samantha Collins sent in a clearly written solution similar to ours, but with more prose to clarify the explanation.

Statistics / Contest #1

Prob #, % Correct (top 5 each school)

1-1    95%1-4    82%
1-2    96%1-5    35%
1-3    33%1-6    56%