ABACUS International Math Challenge
for
3rd and 4th graders
October, 2005
A.497. The marching band could line up
only in rows of 5 people because in rows of 2, or 3, or 4 one person was
always missing from the last row. How many members are in this band if we
know that it is more than 30 but less than 100?
A.498. My grandma harvested all her fruit
in her huge garden. Half of al the fruit was plumb, a fifth was apricot,
and the rest were apples. The apricot and the apples together were 500 kg.
How much of each fruit did she harvest?
A.499. Grandma walked from her house to
the back of her garden to bring some water for the workers. When she walked
half the distance and another 50 meters, she stopped to rest a little. When
she walked half of the rest of the distance and another 50 meters, she stopped
to rest again. Then, finally, when she walked half of the rest of the distance
and another 50 meters, she got to the back of her garden. How far is the
back of her garden from her house?
A.500. How many different ways can you
read the word ABACUS in the following cases:
a) 
b) 
c) 
A.501. For the fall school trip the children
took 2 baskets of apples. At the first snack time they ate half of the apples
in the first basket. "Interesting, if we ate the same amount from the
second basket, only a third of the apples in that basket would be missing,
although it had 2 kg more apples originally than the first basket."
-noticed Kate. How many kg of apples did the children take for this trip?
A.502. My grandpa is a tricky man. He locked
up the cabinet door where my grandma stores all the candies, and then he
put the key in one of three boxes he marked by A, B, and C. Then he wrote
the following sentences on the boxes:
A) The key is not in box B.
B) The key is not in this box.
C) The key is in this box.
Grandpa told me that some of these statements are true, and others are
false, but if, without looking into any of the boxes, I gave him the box
with the key in it, I could have as much candy as I wanted to.
Could you help me to find the right box?
A.503. How can you bring up 6 liters of
wine from the barrels in the cellar if you have only a 4-liter pitcher and
a 9-liter pitcher?
A.504. Grandpa got his barrels ready for
wine-making. He has six 140-liter, one 255-liter and three 115-liter barrels.
Out of 100 kg of grapes he can squeeze 60 liters of juice or he can make
12 kg raisins from it. How many kg of raisins will grandpa have if he has
3200 kg of grapes and he wants to fill up all of his barrels with juice?
Please, send your solutions to: