1A
R1-A Three dice are rolled. The probability that the sum of their points is 14 is
written in the form
p/q
where p and q are relatively prime, find p + q.
1B
R1-B T = TNYWR (The Number You Will Receive). In an acute triangle ABC
with
ACB T
point M is the midpoint of AB. If P and Q are points on BC and
AC respectively such that
AP BC
and
BQ AC
find
PMQ .
Intermediate Level Relay Round 2A
R2-A Find the greatest value of
a b c c a b c
, where a, b, c are the
numbers 2012, 2013 and 2014 in some order.
2B
R2-B T = TNYWR (The Number You Will Receive). Two points A and B stay at
diametrically opposite points on a circle of center O. They start moving in
opposite directions (A clockwise, B anti-clockwise). Point B moves twice faster
than A. They meet for T-th time at some point C. Find the
AOC
in degrees.
3B
R3-B T = TNYWR (The Number You Will Receive). In a group of T students
some pairs of students exchange presents. It is known that there are no three
students A, B and C such that A and B exchange presents; B and C exchange
presents; A and C exchange presents. Find the maximum number of presents given.
3A
R3-A Let
x 3 4 12 3 4 12
. Find 5x
2
.
Intermediate Level Relay Round 3B
R3-B T = TNYWR (The Number You Will Receive). In a group of T students
some pairs of students exchange presents. It is known that there are no three
students A, B and C such that A and B exchange presents; B and C exchange
presents; A and C exchange presents. Find the maximum number of presents given
R1-A Three dice are rolled. The probability that the sum of their points is 14 is
written in the form
p/ q
where p and q are relatively prime, find p + q. 1B
R1-B T = TNYWR (The Number You Will Receive). In an acute triangle ABC
with
ACB T
point M is the midpoint of AB. If P and Q are points on BC and
AC respectively such that
AP BC
and
BQ AC
find
PMQ . 2A
R2-A Find the greatest value of
a b c c a b c
, where a, b, c are the
numbers 2012, 2013 and 2014 in some order. 2B
R2-B T = TNYWR (The Number You Will Receive). Two points A and B stay at
diametrically opposite points on a circle of center O. They start moving in
opposite directions (A clockwise, B anti-clockwise). Point B moves twice faster
than A. They meet for T-th time at some point C. Find the
AOC
in degrees. 3A
R3-A Let
x 3 4 12 3 4 12
. Find 5x
2
.
3B
R3-B T = TNYWR (The Number You Will Receive). In a group of T students
some pairs of students exchange presents. It is known that there are no three
students A, B and C such that A and B exchange presents; B and C exchange
presents; A and C exchange presents. Find the maximum number of presents given.
댓글 없음:
댓글 쓰기