ABACUS International Math Challenge
for
5th and 6th graders
October, 2000
B.201. Write the digits 0, 1, 2, 3, 4,
5, 6, 7, 8, and 9 into the rectangles so that the number created from every
row is divisible by 3. None of these numbers may start with a zero.
B.202. Can you find two 5-digit numbers
containing only odd digits so that the product of these two numbers contains
only odd digits, also?
B.203. There are two 3-meter tall flag
poles. You tie the two ends of a 4.5 meter long rope to the tops of these
poles. The lowest point of the rope is 75 centimeters from the ground in
between the poles. How far are the two poles from each other?
B.204. The sum of a 5-digit and a 4-digit
number is 33190. If you reverse both numbers and add them, you get 48400.
What are the original numbers?
B.205. How many 3-digit numbers are there
in which one of the digits is the sum of the two other digits?
B.206. Yummy baked berry muffins and apple
muffins. By the time her guests arrived she ate the same amount from each
of the kinds of muffins, so the third of the berry muffins and half of the
apple muffins were gone. How many muffins did she have left for her guests
from each kind?
B.207. There are two bags, each containing
3 red, 3 white, and 3 blue balls. Without looking, we take out as many balls
as we can from one of the bags, making sure that we still have at least
one ball from each color in this bag. We put these balls into the other
bag. Now, without looking again, from the other bag we put back into the
first bag the least number of balls necessary to make sure that we have
at least two balls of each color in the first bag. How many balls are there
now in the other bag?
B.208. On a chess tournament you get 1
point for winning a match, a half a point for a tie, and zero point for
losing a match. There were 8 competitors, with a different number of total
points at the end, and the competitor finishing in second place had the
same number of points as the last four competitors all together. What was
the outcome of the match between the competitors finishing on third and
seventh place?
Please, send your solutions to: