ABACUS International Math Challenge
for
5th and 6th graders
February, 2008
B.625. We glued 8 identical regular dice
into a 2x2x2 cube. What is the least number of dots on the outside of the
big cube if the sides of each of the dice have 1 to 6 dots on them so that
any two facing sides have a total of 7 dots on them? (Each of the dice has
6 different numbers of dots on its sides.)
B.626. Lassie decided to go home. It took
him 4 days: the first day he made 5/8 of the whole distance, the second
day he made 1/12 of the whole distance, on the third day he ran 5 km, and
for the fourth day he still had 1/4 of the whole distance. How far was he
from home?
B.627. The station manager at the Hoboken
train station orders to put up a Christmas tree every year. He has 5 different
color light bulbs which can be turned on and off independently from one
another. The manager puts a few light bulbs on the tree on December 23rd.
How many different ways can he pick those light bulbs if he wants them to
light up in a different color combination every day till January 6th?
B.628. One of the famous Hungarian mathematicians
lived all his life in the 19th century. Three of the digits in the years
of his birth and his death are the same. His birth year is a multiple of
17, and the year of his death is a multiple of 31. What year was he born
and what year did he die if you know that he lived for more than 50 years?
(You can get an extra point for his name.)
B.629. The currency in Payland is called
a hollar. The mass of four 20-hollar coins is the same as the mass of five
10-hollar coins. If 1 kg of 10-hollar coins is worth 5000 hollars then what
are 3 kg of 20-hollar coins worth?
B.630. 25 of the passengers on a bus know
how to ride a bicycle, 20 of them know how to swim, and there is no person
on the bus who would not know how to do either. The sum of the digits of
6 times the number of passengers is 3 times as much as the sum of the digits
of the number of passengers. How many passengers can be on this bus? How
many of them know how to ride a bike but do not know how to swim, and how
many of them know how to swim but do not know how to ride a bike?
B.631. What positive whole number could
"a" be if 2/7 < 3/a < 4/9?
B.632. Tom spends 1/4 of his weekly allowance
on Monday, 1/6 of it on Tuesday, 1/8 of it on Wednesday, 1/12 of it on Thursday,
1/24 of it on Friday. This means an average spending of $1.60 a day for
those days. How much money does Tom have left for the weekend?