AMERICAN MATHEMATICS COMPETITIONS
CONTEST AT BELS – FEBRUARY 17, 2016
Each year thousands of students around the world
participate in the American Mathematics Competitions
Contests given in February. This year for the first time,
BELS students joined in the fun. This year over 50,000
students from more than 1400 schools in 28 countries
participated.
Try to solve this question from AMC-10B: The harmonic
mean of two numbers can be calculated as twice their
product divided by their sum. The harmonic mean of 1
and 2016 is closest to which integer?
(A) 2 (B) 45 (C) 504 (D) 1008 (E) 2015
The contest is a 25-question, 75-minute, multiple choice
examination in high school mathematics. No calculators
were allowed.
Our school winner for the AMC-12 was 12th grader
Onur Kağan Coşkun, who also placed in the top 25% of
all students who took the contest throughout the world.
Try to solve this question from AMC-12B: All of the
numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 are written in a 3x3
array of squares, one number in each square, in such a
way that if two numbers of consecutive then they occupy
squares that share an edge. The numbers in the four
corners add up to 18. What is the number in the center?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
Answers: Since the harmonic mean is 2 times their
product divided by their sum, we get the equation
4032
which is then
2017
which is finally closest to (A) 2.
2x1x2016
1+2016
Twenty students from prep through grade 12 were
chosen to participate, based on their math teacher’s
recommendations. Ten students (preps, grade 9s and
grade 10s) took the AMC-10, and ten students (grade
11s and 12s) took the AMC-12.
Our school winner for the AMC-10 was 9th grader
Onuralp Avcı, who placed in the top 25% of all students
who took the contest around the world.
30
THE CLAPPER 2015 - 2016
Draw a 3 x 3 matrix. Notice that no adjacent numbers
could be in the corners since two consecutive numbers
must share an edge. Now find 4 nonconsecutive numbers
that add up to 18. Trying 1 + 3 + 5 + 9 = 18 works. Place
each odd number in the corner in a clockwise order.
Now fill in the spaces. There has to be a 2 in between
the 1 and 3. There is a 4 between 3 and 5. The final grid
should look similar to this.
(C) 7 is in the middle.
1 2 3
8 7 4
9 6 5