ABACUS International Math Challenge
for
3rd and 4th graders
January, 2004
A.409. Uncle Joe has 139 cows on his farm.
Some of them are black and the others are piebald. Last weekend he bought
29 more black cows, so now he has twice as many black cows as piebalds.
How many of each kind of cows does he have now?
A.410. There are 24 tons of hay in one
storage and 32 tons of hay in another. They bring 7 tons of hay to the first
storage and 11 tons of hay to the second storage every day. After how many
days will be 1.5 times as much hay in the second storage than in the first
one?
A.411. Four little ducklings, Jojo, Lili,
Gigi, and Vivi, went to the lake to take a little dip. How many different
ways can they line up on the way to the lake, and on the way back if we
know that Gigi was last on the way to the lake, and that Jojo walked before
Vivi on the way back?
A.412. 6 out of Uncle Joe's 10 chickens
lay an egg every day. The other 4 chickens lay an egg only every other day.
How many eggs do the 10 chickens lay on 20 consecutive days?
A.413. There are 13 ducks, 10 chickens,
and 6 turkeys on the farm. At least how many of these animals must be at
the water fountain if we know for sure that
a) there is a duck or a turkey among them?
b) there is a chicken and a turkey among them?
c) there are at least two different kinds of birds among them?
d) all of at least one kind of birds are there?
e) all of at least two kinds of birds are there?
f) there are at least three birds of at least one of the kind of birds
there?
A.414. 4 black cows and 3 piebald cows
give the same amount of milk in 5 days than 3 black and 5 piebald cows in
4 days. Which kind of cow gives more milk: the black or the piebald?
A.415. Uncle Joe's neighbor has a total
of 25 animals on his farm. He has 3 times as many horses as donkeys, and
twice as many sheep as goats. Not every donkey is the same color. How many
of each animal does he have?
A.416. Uncle Joe's fenced around vegetable
garden has a rectangular shape, and one of its side is three times as long
as the other. The perimeter of the garden is 160 meters. He decided that
he wants a bigger garden, so he is planning to double each side of the garden.
How many times greater will the area of the garden be? How many more meters
of fence does he need to buy if he wants to fence around the whole new garden
using up the old fence again, as well?
Please, send your solutions to: