ABACUS International Math Challenge
for
3rd and 4th graders
November, 2006
A.553. Dr. Foot prescribed a medication
for Johnny for his stomach ache. Johnny has to take the first pill at noon,
and then take one pill every half an hour so that he would take the last
pill at 3:30 pm. If you buy this medicine by the pills, it costs 15 cents
a pill. If you buy it in sheets of 5 pills it costs 60 cents a sheet, and
if you buy it in sheets of 10 pills it costs $1.10. How should Johnny buy
the medicine he needs if he wants to spend the least amount of money. (He
cannot sell the pills he did not use, he has to throw them away.)
A.554. As part of a health drive, the animals
in the forest organized a running race. They had to run on a circular path
and after every lap the last place runner had to drop out of the race, everybody
else kept on running. How many laps did Kanga have to run if he finished
on 10th place out of the 100 participants?
A.555. On a meadow in the forest birds
and rabbits are talking. There are 6 more birds, yet the number of rabbit
legs is 6 more than the number of bird legs. How many birds and how many
rabbits are on the meadow?
A.556. Hyppo started a 4-week diet. At
the end of the first week he lost 30 kg, a seventh of his weight. During
the second week he lost half the amount he lost during the first week. During
the third week he lost a third of the weight he lost in the previous week.
By the end of the fourth week he reached his goal of a weight of 140 kg.
How much did he weigh at the beginning of the diet and how much weight did
he loose in the fourth week?
A.557. On a Saturday afternoon Winnie the
Pooh and Tigger tried to relax in the Chess Club of the forest. They both
played a few games. To his own greatest surprise, Winnie the Pooh won twice
and tied 3 times. Tigger won 3 times and lost 3 times. How many games could
the two of them play all together?
A.558. Turtle was reading an interesting
article in the Newsbell of the neighboring forest. Next day he shared the
news with 3 other animals, the following day those 3 shared it with 3-3
new animals, who have not heard of the news yet, and so on. How many animals
knew the news by the end of the 5th day? How many days did it take for all
1000 animals in the forest to learn of the news?
A.559. In his boredom, the elephant started
to count how many triangles he can see on the back of the turtle (see the
diagram below). How many triangles can You see?
A.560. Turtle is still moving very well
even if he is going to be twice as old in 20 years as he was 20 years ago.
How old is he now?
Please, send your solutions to: