ABACUS International Math Challenge
for
3rd and 4th graders
February, 2004
A.417. Sam and Tom are playing with 9 disks,
which they numbered from 1 to 9. "Interesting! If I take this disk,
I can arrange the rest of the disks into 3 groups so that the sum of the
numbers of the disks in each group is the same." - said Tom. "Hey,
I can arrange those 8 disks in 4 groups, also, so that your statement is
true again." - said Sam. Which disk did Tom take out? Give an example
for the 3 and the 4 groups.
A.418. Yummy took a walk to the black berry
bushes. He picked 648 g of berries, but gave Smarty 2/3 of the berries,
gave Funny 2/3 of the remaining berries, then gave Cuty 2/3 of the rest,
and kept whatever he had left. How much black berries have left for Yummy?
A.419. Seven dragons live in Dragontown.
Every dragon has a different number of heads, and the most heads the 7-headed
dragon has. Every head on every dragon is numbered from 1 to whatever number
is necessary to count every head on each dragon. The number on the head
also indicates the number of teeth in that head. How many heads and how
many teeth do the 7 dragons have all together?
A.420. Can you cut a triangle or a quadrilateral
into more pieces with 3 straight lines? Describe the cuts with a diagram
or otherwise.
A.421. A rectangular land is divided
into 6 square shaped sections, as shown on the diagram. The side of the
smallest square is 1 meter. How long is the side of the greatest square,
e?
A.422. Replace the letters with digits,
so that different letters mean different numbers, but the same letters mean
the same numbers.
A.423. There are 3 trees in the garden.
The 3 trees have a total of 360 kg of fruit on them. The apple tree and
the pear tree together have twice as much fruit on them than the peach tree.
The apple tree and the peach tree together have 60 kg more fruit than twice
the fruit on the pear tree. There are 20 kg more peach than pear. How many
kg of each fruit is there on each tree?
A.424. Create a magic 3x3 grid containing
nine consecutive numbers so that the sum of the numbers in each column,
row and diagonal is 2004.
Please, send your solutions to: