The
competition is done in two individual phases and one team phase.
Each student does Phase I and Phase II individually, and each team of
four students does Phase III.
Phase
I: A 40 minute, 30
problem test, where calculators are not allowed. The questions
are relatively short, but most have both a brute force method and an
elegant method of solution. Using elegant methods allows a
student to save time for the harder questions that come toward the end.
Sample
Problem: What is the
greatest number of possible points of intersection for eight distinct
lines in a plane?
Phase
II: A 4-part, 8
problem test, with two problems per part. Students are allowed 6
minutes for each part. These questions tend to be longer and more
involved problems, often incorporating a calculation. Calculators
are allowed for this phase.
Sample
Problem: Two distinct
numbers are selected simulataneously and at random from the set {1, 2,
3, 4, 5}. What is the probability that their product is an even
number? Express your answer as a common fraction.
Phase
III: A 20 minute team
phase, where each team of four students works together on a group of
ten problems.
Sample
Problem: The measures
of the four interior angles of a quadrilateral are x, 2x, x+20 and x+40
degrees. How many degrees are in the measure of the smallest
interior angle of the quadrilateral?
Scoring
The total score for each
individual is the sum of the Phase I score and twice the Phase II
score, giving a maximum of 30 + 2x8 = 46.
The team score is the average of the four individual total scores, plus
twice the Phase III score, giving a maximum of 46 + 2x10 = 66.
The Countdown Round and Final Results
The team's score is ranked
with respect to the other teams, and the top three teams in our region
earn trophies and the right to move on to the state level
competition. The individual scores are ranked against the
other individual scores, and the top ten scores among all the schools
compete in a head to head exciting Jeopardy-like countdown round. Two students compete at a time,
starting with numbers 9 and 10. Questions appear on a screen and
the first to buzz in with the three correct answers stays alive for the
next round, and number 8 is brought into compete etc. Calculators
are not allowed, but scrap paper and pencils are allowed. The
pace is frantic, and the excitement intense. Usually each problem
is answered in less than a few seconds. When the number 1
scoring student is finally brought in to compete, the winner of that
round concludes the competition. The last three individuals to have
survived win prizes and trophies. The national level countdown round
is covered by ESPN, and shown in an hour long special.
Sample Problem: What is the greatest integer value of n such that
3n < 10,000?