ABACUS International Math Challenge
for
3rd and 4th graders
March, 2002
A.305. Susie is chasing butterflies in
a meadow. Accidentally she ran into a pear tree, and knocked half of the
pears off the tree. Since she loves pears, she shook the tree again and
knocked a third of the rest of the pears off. Now there are 10 pears left
on the tree. How many were there on it originally?
A.306. The king's carpenter had to frame
3 pictures of the young prince. Each picture is 30 cm wide and 40 cm tall.
However, in the storage room there was lumber of the following lengths only:
170, 180, 190, 210, 220, and 230 cm. After a little thinking, the carpenter
picked up two pieces of lumber, cut them up to have just the right size
pieces enough for the 3 frames without having any leftover. Which two pieces
of lumber did he pick and how did he cut them up?
A.307. There were 42 people at a party.
The first girl said that she danced with 7 boys, the second girl said that
she danced with 8 boys, the third girl said that she danced with 9 boys,
..., and the last girl said that she danced with every boy. How many boys
were there at the party?
A.308. Kathryn, Lauren and Gina are competing
on a ski team. There are 6 races in the season. They all want the 1st place
trophy, (especially Kathryn). They get points for a 1st, 2nd, or 3rd place
finish in their 4 best races. A first place finish is worth 25 points, second
place 15 points, and 3rd place 10 points. They have held three races so
far. Kathryn has 2 first places and 1 second place. Lauren has 1 first place,
1 second place, and 1 third place. Gina has one second place and 2 third
places. After how many more races can Kathryn be guaranteed to be the only
winner of the trophy? Is it possible for Kathryn and Lauren to tie for the
trophy? Is it possible for Lauren and Gina (without Kathryn) to tie for
first place?
by Kathryn Dawson, New York
A.309. Two native Americans are sitting
in a boat. One of them says:
"You are my son, but I am not your father."
How could this be?
A.310. The little chefs are putting a 2-digit
number of donuts on a serving plate at a party. If they put the donuts in
groups of three they have two left over. If they put them in groups of 4
they have 3 left over. If they put them in groups of 5 they have 4 left
over. How many donuts did they make?
A.311. Every afternoon Susie enters the
palace through door B and goes through all 9 rooms using every door exactly
once, finally stopping in the prince's room to read him a story. Which number
indicates the prince's room?
A.312. A vendor has 15 bags of different
tea leaves with an average of 280 grams of leaves in a bag. After he sold
a whole bag, the average mass of the rest of the bags became 285 grams.
How many grams of tea leaves were in the bag that he sold?
Please, send your solutions to: