ABACUS International Math Challenge
for
5th and 6th graders
November, 2007
B.601. Ann and Bea weigh 22 kg together,
Ann and Cecilia together weigh 28 kg, while Bea and Cecilia together weigh
36 kg. How much do they each weigh alone?
B.602. How many 3-digit positive whole
numbers do not contain the digits 2 and 9?
B.603. Agnes, Sylvia, Pete and Leslie are
classmates. They all have different family names: Smith, Miller, Taylor
and Woo. In each of the following pairs of names one name is correct, but
the other is not. What are the correct names?
a) Leslie Smith and Sylvia Miller
b) Leslie Miller and Sylvia Taylor
c) Agnes Miller and Pete Taylor
B.604. The calculator uses 7 lines to show
the digit 8. (See the diagram.) The other digits are shown by using some
of these lines, as we know. Some of the 2-digit numbers are shown on the
calculator by using exactly as many lines as the sum of their digits. How
many such 2-digit numbers are there?
B.605. A tea factory puts a little card
in each tea box that either says Bermuda, Hawaii, or Fiji. If you send in
4 cards saying Bermuda, or 3 cards saying Hawaii, or 2 cards saying Fiji,
you can participate in a lottery and win a trip to the island on the card.
How many boxes of tea do you have to buy at least if you want to participate
in the lottery for sure?
B.606. On a farm they keep black and white
goats and black and white sheep. Two sheppards take 50 animals out of them
to the meadow. On the way there, one of the sheppards counts the number
of white animals, and the other sheppard counts the number of sheep. From
these two numbers they want to know how many black goats and white goats
and how many black sheep and white sheep are there with them. Give an example
when they can, and give an example when they cannot do it.
B.607. There are five unicorns in a zoo
eating a total of 5 rolls of hay every week. Every white unicorn eats 2
rolls of hay a week, every black unicorn eats a half a roll a week, and
every Asian unicorn eats a quarter of a roll of hay every week. How many
white, black and Asian unicorns are there in this zoo?
B.608. What is the angle between the two
hands of an analog clock at 10 minutes past 6 o'clock?