**Which Calculators Are NOT
Allowed? **Our contests do

**Future Contest Dates and our
Algebra Contest **Our final contest is Apr. 13. This is year
6 of April's *Algebra Course I Contest*. To participate,
write for information.

**Rescheduling A Contest &
Mailing Results **If you have **school closings or testing
days**, our rules allow an alternate contest date. We prefer
the **previous week** so we get results on time. Mail scores
by Friday of the official contest week. If scores are late for
due cause, attach a brief explanation. Late scores unaccompanied
by such an explanation are not normally accepted.

**Next Year's Contest Dates
**will be held on these Tuesdays: Oct. 26, Nov. 30, Jan. 11,
Feb. 8, Mar. 7, and Apr. 11. We also sponsor contests for grades
4, 5, 6, 7, 8 and *Algebra Course I*.

**End-of-Year Awards **Engraving
of awards begins Apr. 26. We give awards to the 2 schools and
2 students with the highest totals in the entire League and to
the school with the highest score in each region. *Winning schools
must postmark their results by Apr. 16*. Results postmarked
later *cannot* be used to determine winners. Completion of
the cumulative column is optional, but student awards are based
only on scores *regularly* listed in that column. (Student
certificates of merit were enclosed with Contest 5.)

**General Comments About Contest
5 **Linda Sadler said "This was more difficult than the
other contests this year." Ted Heavenrich said "A good
contest! Certainly more challenging than the last one." Jim
Beam was surprised his school "didn't have several perfect
papers" since none of the problems seemed especially difficult."
Dwight Williams said contest 5 had "a good variety of questions."
Joe Holbrook called it "A good competition." Dylan wrote
that he had averaged 3 or 4 last year, but was averaging 5's this
year. He thought we should make the questions more difficult.
Dave Stouffer said "Thanks for another set of well-balanced
questions which require a student to have a reasonable command
of the fundamentals and the capacity to read a problem for *exactly
what it says* and not what the student wants it to say."
Karen Holmes said "we are enjoying the monthly competitions
although we did not fare well on contest 5." Suzanne Moll
said "This contest was harder, but the students enjoyed it.
Most scores were low, and there were not too many 4's." Cathy
Heideman said "Thanks for all the great questions! Contest
5 was a real challenge for my students." Sheryl Cabral wrote
"This is our first year, and my students and I are very excited
about it. The problems are challenging but accessible, and all
participants understand the solutions when we go over them."
Student Allen Piscitello said he has been taking our contests
since 5th grade. As a freshman, he got only 2 or 3 right on each
HS contest. As a senior, he has gotten all but 1 of the first
30 correct. *Congratulations, Allen!* Elizabeth Kannegaard
said her students thought the League "has gotten a wee bit
too easy this year. We enjoyed our lower scores and beefier questions."
Irene Stein said "Thanks for a great year so far." Mary
Lynn Mallen said "What an unusual contest. More students
got #6 right than #4 or #5. Good problems, though." Jerry
Detweiler asked "What happened to the order of difficulty
6, 5, 4, 3, 2, 1?"

**Problem 5-1: Comments **Brenda
Mason said this was the worst her students had done on a #1 question.
One advisor said that many of her students thought that, in the
ordered pair (*a*,*b*), *a* and *b* were distinct,
She felt "problem #1 was poorly written."

**Problem 5-3: Alternate Solutions
**Travis Bower said "Another way: use a clock as a model.
Subtract opposite numbers, then double." For example, there
are 2(9-3) = 12 numbers on a clock. There are 2(99-19) = 160 students.
Dave Farber doubled the # from 19 to 98, inclusive, to get 2(98-19+1)
= 160.

**Problem 5-4: Comments And
An Appeal (Denied) **Dwight Williams, Lorna TenEyck, Leo Polovets,
Jerry Detweiler, J. Shaw, and Ken Brien, all noticed what Mary
Lynn Mallen noticed: "In #4, most kids treated the problem
as if the domain were the natural numbers." Sheryl Cabral
said "I believe that teaching our students precision in vocabulary
is essential, but I'd rather do it somewhere other than on a contest."
Numerous appeals sought credit for an answer of 3/9 or 3/10, based
on treating the domain as the natural numbers. The appeal was
denied by Prof. Brian Conrad of Harvard University's Math Department.
R. Whirl asked "Is the probability [1,3]/(0,10) *really*
2/10, since the interval 1£*x*£3 includes both
endpoints, while 0<*x*<10 includes *neither*?"
The answer is "yes." Since a single point has no dimension,
it has no length. Its presence or absence has no effect on the
length of an interval. This topic is called *geometric probability*.
The number of possible outcomes is infinite, so you can't compute
the ratio (favorable #)/(total #) Instead you must use
ratios of lengths (or sometimes ratios of areas). Jim Beam and
Bruce White independently said it would have been clearer to have
used the words *positive real number* in the question statement.
Thanks for a great suggestion!

**Problem 5-5: Appeals (Denied)
**Numerous appeals claimed that, since 10* ^{n}*
and log

**Problem 5-6: Comment **Ted
Butler & Linda Sadler said the following solution led *many*
students to the right answer using wrong reasoning: Area = 49
= 7^{2}, so *r* = 7 and arclength = 14. David Sutleff
& Dave Farber sent the same alternate solution.

Problem #, % Correct (top 5 each school)

5-1 82% | 5-4 33% |

5-2 70% | 5-5 34% |

5-3 81% | 5-6 44% |