ABACUS International Math Challenge
for
7th and 8th graders
November, 2002
C.337. There are 5 identical circular disks
placed on the table as shown below. With a straight line, divide in half
the united area of the 5 disks.
C.338. Grandma bought 2 candles. The red
is 1 cm longer than the blue candle. In the afternoon of the Day of Christmas
at 17:30 she lit the red candle, at 19:00 she lit the blue candle, also,
and let them burn until they were finished. The two candles had the same
length at 21:30. The red was finished at 23:30, and the blue was finished
at 23:00. How long was the red candle originally?
C.339. Is there any other polyhedron besides
a cube which has only square sides?
C.340. Which number is greater: 
or 
?
C.341. Andrew's 9-digit secret code starts
with 381, and contains every non-zero digit. He created this number so that
the number created from the first two digits of his code is divisible by
2, the number created from the first three digits of his code is divisible
by 3, the number created from the first four digits of his code is divisible
by 4, and so on until 9. What is his secret code?
C.342. In the 6th, 7th, 8th, and 9th games
of the season a basketball player scored 23, 14, 11, and 20 points respectively.
His average points after the first nine games was greater than after the
first 5 games. At least how many points did he have to score on the 10th
game if his average for the season became higher than 18 points after the
10th game?
C.343. The digits of a 4-digit number from
left to right are odd, even, odd, and even. When you double this number,
you get a number which contains only even digits, but only the last digit
of half of the original number is even. Find all of these 4-digit numbers.
C.344. Is it true that if every side of
a convex hexagon is greater than 1 cm, then it has at least one diagonal
that is longer than 2 cm?