ABACUS International Math Challenge
for
5th and 6th graders
October, 2006
B.545. I painted a 4x5x5 column green,
then I cut it into unit cubes by plains parallel to the sides of the column.
How many of these unit cubes have exactly 0; 1; 2; 3; 4; 5; and 6 green
sides?
B.546. Grandma has 2 grandsons. One digit
of the 2-digit number indicating grandma's age is the age of one of her
grandsons, the other digit is the age of her other grandson. The sum of
these 3 ages is 63. How old is grandma?
B.547. Find the 4-digit number abcd
so that the sum of the four numbers abcd + abc + ab
+ a = 2006.
B.548. There are 400 grams of tea leaves
in a box and you have to put them in 40-gram bags. For doing this you have
a 2-arm balance without a scale on it, and a 100-gram and a 180-gram weight.
Get the job done by taking no more than 9 measurements.
B.549. Which number is greater and by how
much: 2/3 or 200001/300001?
B.550. The 3-story house of cards on the
picture is built by using 15 cards. Using the same method, how many cards
do you need to build a 31-story house?
B.551. In the parking lot of a shopping
mall they store the shopping carts as shown on the diagram. How many centimeters
long is a cart if the total length of 10 carts stored is 290 cm, and the
total length of 20 carts stored is 490 cm?
B.552. Two numbers are called a mirror
number pair if the order of the digits of one of the numbers from left to
right is the same as the order of the digits of the other number from right
to left. The product of which mirror number pair is 92565?