ABACUS International Math Challenge
for
5th and 6th graders
January, 2002
B.289. Imagine a city with a central metro
station from which the metro lines are running in straight lines in different
directions. Every line has 12 stations on it. The final stops (different
from the central station) of these metro lines are connected with a circular
metro line with no additional station on it. This metro line has 11 stations.
How many stations are there all together in this metro system?
B.290. We divided the sides of a square
into different numbers of equal sections. As the diagram shows, we connected
three divider points. What part of the area of the square is the area of
the shaded triangle?
B.291. In the following multiplication
(symbolized with x) the same letters mean the same digits, and different
letters mean different digits. What are the values of the letters?
NET x N x EE x ET = NETNET
B.292. We checked the list of the students
in a Math Club. Everybody had a different full name, but we found only the
following first names: Andrea, Gabe, Eric, Rita, Martin, Zaak, and Julia,
and only the following last names: Smith, Taylor, Sheppard, and Goldstein.
How many members could this Math Club have?
B.293. We placed 15 discs as shown on the
diagram. The perimeter of a disc is 12 cm. How long is the outside perimeter
of this figure?
B.294. A helicopter flies 500 km North
from New York. Then it turns West and flies 500 km. There it turns South
and flies 500 km, then it turns East and flies 500 km. At that point he
runs out of fuel and has to land. The pilot radios the airport he started
from for help. What direction from the airport is his location in?
B.295. In a complete set of dominoes on
both halves of every domino there could be zero, 1, 2, 3, 4, 5, or 6 dots.
How many pieces are there in a complete set containing one of each kind
of dominoes? Can you create a closed ring using all of the pieces following
the rule of the game that you may place one end of a piece to the end of
an other piece if these ends have the same number of dots on them?
B.296. The archeologists are working on
an excavation site of a Roman marketplace. They know that the marketplace
is square shaped, was surrounded by 4 walls, there was a well in the middle
of the marketplace in which the merchants poured their gold in case of a
barbarian attack. The archeologists found one corner of the marketplace
marked by a 1 meter long section of both walls running from this corner,
and a marking pole that was placed next to one of the walls running into
the diagonally opposite corner of the one they found already. How can the
archeologists locate the well with all the gold in it?
Please, send your solutions to: