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

**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

**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."

Problem #, % Correct (top 5 each school)

3-1 96% | 3-4 71% |

3-2 90% | 3-5 75% |

3-3 74% | 3-6 33% |