ABACUS International Math Challenge
for
3rd and 4th graders
February, 2003
A.361. As he was traveling, Gulliver always
loved to watch the animals playing in the ocean. One day he saw sharks on
the West side of the ship, dolphins on the East side, and sword fish on
the North. How many of each of these animals did he see if he saw a total
of 54 dolphins and sword fish, a total of 35 sword fish and sharks, and
a total of 49 sharks and dolphins?
A.362. On the Land of the Giants Gulliver
had to hurry to keep up with the giants. While a giant made three steps,
Gulliver had to make 15 steps. How many steps did Gulliver have to make
from the ship to the king's castle, if a giant would have to take 42 steps
on that distance?
A.363. Captain Cook and Captain Hook start
to sail towards each other at the same time from a distance of 200 miles.
Captain Cook's ship would make the whole distance in 4 hours, but it would
take Captain Hook's ship 5 hours. How far are they from each other after
2 hours if each ship sails with a constant speed?
A.364. At the market in Lilliput the merchant
has a two-arm balance and three weights: a 1-gram, a 3-gram, and an 8-gram
weight. Find all those weights (with a whole measuring number of grams)
that can be measured with his equipments.
A.365. On the Land of the Giants a wonder
plant that grows towards the skies brings 5 new flowers every second, and
it grows 50 meters in every 5 seconds. How many new flowers does it bring
while growing 100 meters?
A.366. The people of Lilliput made a blanket
for Gulliver out of the various pieces of cloths they had. What is the area
of the ABCD rectangular shaped blanket if the area of the AEFK square shaped
piece is 4 units, the area of the GHCL square shaped piece is 9 units, points
E, F, G, and H are on the same straight line, and the FG segment is 5 units
long?
A.367. On the square shaped sails of three
ships you can see the following dark triangles. What part of the area of
the whole sail is the area of the triangle on each sail?
A.368. They put a few boxes of fruit on
Gulliver's ship, also. The chef was told that the mass of one box of plumbs
plus one box of pears is the same as the mass of 5 boxes of apples. The
mass of one box of pears is the same as 4 boxes of grapes. The mass of 2
boxes of grapes plus one box of pears is the same as the mass of 3 boxes
of apples. The chef now is calculating how many kilograms is one box of
plumbs, one box of pears, and one box of apples, if he knows that there
are 3 kilograms of grapes in one box?
Please, send your solutions to: