ABACUS International Math Challenge
for
5th and 6th graders
March, 2004
Please, send your solutions
in by May 15, 2004.
B.425. Fred and George are playing a game
where the first person says a number under 5. Then the other person can
add any number between 1 and 10 to that number. They keep going until one
person says 100, then that person wins. Is there a winning strategy for
the person who starts the game?
by Ajay R. Ravindran
B.426. In the figure below, AB, AE, EC
and CD are straight lines. AB and CD are parallel. What is the sum of the
following three angles?
angle BAE, angle AEC, and angle ECD
by James Li
B.427. Write addition, subtraction, multiplication
signs or nothing between the digits 123456789 so that the equality is true:
123456789=2004
B.428. In the following multiplication
problem, fill in the missing numbers:
by Akhil Vohra
B.429. Today all of farmer Bill's chickens,
ducks and geese laid one egg. Bill has twice as many chickens as ducks,
25 more chickens than geese and 3 more ducks than geese. The weight of a
goose egg is twice as much as the weight of a chicken egg. It's also triple
as much as the weight of a duck egg. The weight of three chicken eggs is
75g more than the weight of one goose egg. What's the weight of the eggs
Bill's chickens, ducks and geese laid all together today?
by Michael Schubert
B.430. 8 people wish to form pairs and
play a card game called Bridge. How many games are needed so that all possible
teams play each other?
by Jack Dillon
B.431. I rolled a regular dice (which is
a cube that has the numbers from 1 to 6 on its sides, so that the sum of
the numbers on the facing sides is always 7) 10 times. The product of the
10 numbers I rolled is 7776. What is the highest possible sum of these 10
numbers.
B.432. Several consecutive sheets fell
out of a thick book. On the sheets that fell out, the lowest page number
was 387, and the highest page number on these pages had the same digits
of 387 but in a different order, of course. How many sheets did fall out
of the book?
Please, send your solutions to: