ABACUS International Math Challenge
for
5th and 6th graders
February, 2004
B.417. Sam transferred an ever-growing
bean plant into his garden from the greenhouse. On the first day the plant
grew a half of its original height. On the second day it grew 1/3 of its
height at the beginning of that day. On the third day it grew 1/4 of its
height at the beginning of that day, and so on. How many days did it take
the plant to grow until it became as tall as 100 times its original height?
B.418. I have more than 2 animals at home.
All of them are dogs, except for 2. All of them are cats, except for 2.
All of them are hamsters, except for 2. What kinds of animals and how many
of each animal do I have?
B.419. There are 5000 families living in
the village of Neverfind. Every family has no more than 2 dogs. Most families
have one dog, and half of the rest of the families have no dogs at all.
How many dogs are there in Neverfind, if there are no homeless dogs?
B.420. Corina asked John: "How old
are you?" John said: "2 days ago I was still 16 years old. Next
year I will turn 19." What is John's birthday, and what day of the
year did Corina ask him this question?
B.421. Two friends are competing in The
ABACUS International Math Competition. If the first one had half the points
he has, and the second one had half more than what he has, then the first
one had 1/3 of the points of the second one. Who is ahead of the other now
in the competition?
B.422. John, Frank and Peter are competing
in a league of the three of them. Everybody plays the same number of games
with everybody. There is no tie, somebody always wins a game. Frank won
twice against Peter and four times against John. John won four times against
Peter and three times against Frank. Peter won 5 times against Frank and
three times against John. How many games were there all together, and how
many games did each player play?
B.423. Quadrilateral ABCD is a parallelogram.
Its area is 24 area units. M and N are the midpoints of sides AD and BC.
What is the area of triangle OQP?
B.424. Vera has a lucky 2-digit number.
When she multiplies the two digits, she gets half of the number. What is
her lucky number?
Michael Do, Sydney, Australia
Please, send your solutions to: