ABACUS International Math Challenge
for
5th and 6th graders
November, 2008
B.657. Olga has a bag of balls, 10 of them
are red, and the other 12 are white. She pulls a ball out of the bag. If
it is red, she puts it back and puts another 5 red balls into the bag. If
it is white, she puts it back and she puts 3 more white balls into the bag.
When, after putting the balls into the bag, she has exactly 43 balls in
the bag, she stops. How many red and how many white balls does she need
to pull for this to happen?
B.658. Your digital clock shows the time
from 00:00 till 23:59. At 5 minutes passed 3 o'clock in the afternoon you
see 15:05 showing on your clock. If you consider this to be a division then
the quotient is 3 and the remainder is zero. How many such times are there
in a day when the "quotient" is a whole number and the remainder
is zero?
B.659. You may use two kinds of square
shaped tiles: the sides of the red tiles are 20 cm, the sides of the blue
tiles are 10 cm. Using a total of 6 tiles, make a bigger square. How many
blues tiles can cover this bigger square?
B.660. You have 64 identical red cubes.
You paint one of them blue, and then you make a 4x4x4 cube using all 64
of them. How many different cubes can you possible make if those big cubes
that can be rotated into the same position are not considered to be different?
B.661. Write down every 2-digit number
in an increasing order in one line by using red, blue and green colors continually
in this order for every digit. Did you have to write every digit in every
color?
B.662. On the diagram, below the perimeters
of the identical rectangles are 16 cm, and the area of the small square
in the middle is 16 square centimeters. How big is the area of each of the
identical rectangles?
B.663. In how many 4-digit numbers is the
sum of the digits 5?
B.664. Divide the numbers 2, 3, 4, and
5 into two groups of two numbers so that the sum of the products of the
numbers in each group is the smallest possible number.