ABACUS International Math Challenge
for
3rd and 4th graders
February, 2006
A.529. Sally is organizing her dolls. She
puts most of them on the top of her cabinet, but a third of them do not
fit there. So she puts two of those on her desk, and the rest she puts on
three shelves, 17 dolls on each shelve. How many dolls does Sally have?
A.530. Hector loves climbing on the playground.
He is standing on the middle step right now. He makes two steps down, then
5 steps up and seven steps down again. This way he got to the bottom step
of the climber. How many steps does this climber have?
A.531. Tony is playing with colored glass
balls. There are 12 red and 8 blue balls in the box. He takes balls out
of the box randomly.
a) How many balls does he have to take out to have two consecutive red
balls taken out?
b) How many balls does he have to take out to have two consecutive blue
balls taken out?
A.532. Camille is playing with her red
disks. She put the 16 disks tight on a 4x4 grid. Then she took 6 disks off
the grid so that there is an even number of disks in each of the horizontal
rows and vertical columns. What is the arrangement of the remaining disks?
A.533. In a target throwing game 5 children
are throwing two stick balls at the same target board. You can get points
between 1 and 10 for each throw that hits the board according to how close
to the center they hit the board. Each throw hit the target board but no
two balls hit the same value area. At the end of the game the children had
the following total numbers of points: Bea had 11 points, Lia had 4, Sandy
had 7, Rich had 16, and Danny had 17 points. Who got how many points for
each of their throws?
A.534. Ben is putting pieces on the fields
of a chess board. At least how many pieces did he use if we know that in
any arrangement of these pieces there is a row or column with at least 3
pieces in it?
A.535. Tom and Jerry are playing with a
cube. They wrote the following numbers on its sides: 0, 1, 3, 4, 5 and 9.
You can see the cube in three different positions on the following diagram:
What numbers are there on the bottom of the cube in those positions?
A.536. There is a rectangular playground
in Tony's backyard. One side of it is 3 times as long as the other. There
is an 80 cm wide side walk around it, which is covered by 496 square tiles.
The side of these tiles is 4dm. What is the area of the playground in square
meters?
Please, send your solutions to: