ABACUS International Math Challenge
for
3rd and 4th graders
September, 2004
A.433. In a concert the pianist was sitting
on a three-legged seat, the 24 violinists and the 12 flutists were sitting
on 4-legged seats, the 2 base players and the conductor were standing. How
many legs could you count on this concert if there were no other participants
on stage?
A.434. The people of Etown organized a
Day of Food-sampling. They wanted three different categories of food (fish,
pasta, and wild meat) presented at three different locations (one category
at each restaurant). Four restaurants (The Hunter, The Fishermen, The Crown,
and The Wildchase) applied to be hosts of the event. At The Hunter they
make only pasta and wild meat dishes, at The Fishermen they make only fish
and pasta dishes, at The Crown and at The Wildchase they make all three
kinds of dishes. How many different choices did the organizers have to pick
3 of the 4 restaurants with their one category of food?
A.435. Kate bought little presents for
her sisters at the flee market. She noticed that the amount of money she
had to pay at one of the stands contained the same two digits as the amount
she paid at the previous stand, but in the reversed order. The sum of these
digits was 13, and she paid $27 less at the previous stand then now. She
paid with a $100 bill at each stand. How much change (money) did she get
back at each stand?
A.436. There is a huge two-armed balance
at the Fair, which can measure the weight of the children. When Andy and
Fanny set together on the same side, they had to use 82 kg to balance them
out. When they set on different sides, they had to put 12 kg next to Andy
to balance them out. What are the weights of Andy and Fanny in kg?
A.437. Kate wants to send a birthday card
for her grandfather. She can pick one from 167 different cards. She can
put the card in either a blue or a white envelope. She can write using either
a blue or a black pen. She can pick one out of 3 stamps. How many different
cards could she send to her grandfather?
by Zsuzsa Bognár, Hungary
A.438. There are 3 sectors (A, B, and C)
in a sports stadium. Sector A is twice as expensive as Sector B, and three
times as expensive as Sector C. The children's tickets are half priced in
every section. How much does in cost for two adults and two children to
sit in Section B if it costs $242 for four adults and three children to
sit in Section C?
A.439. The Strongest Man of Etown had to
roll a huge rock ball 10 meters. The spectators may guess the weight of
the ball. Four people gave the following guesses to the organizers: 196
kg, 163 kg, 178 kg, and 185 kg. One guess was 1 kg off, one was 6 kg off,
one was 17 kg off, and one was 16 kg off. How many kg was the weight of
the ball?
A.440. The most exciting event in the town's
Sports Festival is the soccer tournament. The team of the Bonecrushers started
rather badly. They scored only one goal in their first 5 games, but to their
credits, they received only two goals. How many points could they have the
most and the least if a team gets 3 points for a victory, 1 point for a
tie and the loser team does not get any point?
Please, send your solutions to: