ABACUS International Math Challenge
for
5th and 6th graders
October, 2007
B.593. After saving their money for a long
time, Peter and Polly went in the same toy store and fell in love ... with
the same toy. Peter cannot buy it because he is missing $470. Polly cannot
buy it because she is missing $30. Even the two of them together do not
have enough money to buy it. How much could the toy cost if we know that
its price in dollars is divisible by 10?
B.594. In a game you have to collect treasures.
There are 8 kinds of treasure, and three of each kind. If you have only
one of the treasures of a kind, it is worth 1 point. If you have two of
a kind, they are worth a total of 3 points, but if you have all three of
a kind, they are worth 6 points. Pete has 9 treasures. How many points could
they be worth at least and at most?
B.595. Tom's family is building a house.
In his room, Tom would like to have a rectangular window divided into 12
small squares in a 3x4 arrangement. 2 of the 12 glasses are opaque, so you
cannot see through, the others are clear. How many different windows can
Tom design for himself if he wants the window to look the same from the
inside as from the outside?
B.596. In Neverland the pirates use small
cannons to capture a castle on an island. The pirates are excellent shooters,
so they can shoot exactly where they want to. In the castle there is only
one big cannon sitting well-hidden on the top of the front wall, so the
small cannons of the pirates cannot hit it directly. The weak point of the
castle is that if the front wall is hit on 280 well-aimed points then the
wall collapses while the cannon falls with it and becomes useless. This
way the castle can fall into the hands of the pirates. The pirates fire
their cannons one after another, and when all of them took a turn, the big
cannon in the castle fires and takes one of the pirates' cannons out. At
least how many cannons do the pirates have to bring into the attack if they
want to capture the castle? How many of those cannons will survive the attack?
B.597. Somebody described a number the
following way:
23 million 23 hundred thousand 23 thousand 23 hundred 23.
What is the greatest 2-digit divisor of this number?
B.598. Find 5 different positive whole
numbers so that the sum of their reciprocals is 1.
B.599. Two runners with constant speeds
start running at the same time from the two ends of a long straight street.
They meet twice, once at 800 meters from one end of the street, and then
at the other end of the street. How long is the street?
B.600. The ratio of Tom's and Jerry's money
is 5:3. If Tom spends $160 of his money, the ratio becomes 3:5. How much
money did they have originally?