ABACUS International Math Challenge
for
5th and 6th graders
February, 2005
B.473. Steve's rectangular shaped window
is divided into 3x3 smaller sections. Steve paints a few of those sections
yellow so that the whole window looks just the same from the outside than
from the inside. How many different ways can he do this if he paints yellow
a) 2 sections
b) 3 sections?
B.474. Find the 2005th digit to the right
of the decimal point in the expansion of 1/13.
B.475. A person is considered to be lucky
if his/her 8-digit birth date is a palindrome number. (A number is a palindrome
if it is the same when read backwards.) In the 8-digit birth date the first
4 digits are for the year, the next two digits are for the month and the
last 2 digits are for the day. (The day and the month are always written
by 2-digit numbers.) How many such birth dates are there in the spring months
of the year between the years 1000 and 2005? When is the next such birth
date?
B.476. It takes a bus 30 minutes to go
from A to B. There is a bus leaving every 2 minutes from A. At the same
time with a bus, a car leaves from A. It takes the car 7.5 minutes to get
to B. How many buses did the car pass on its way to B?
B.477. What are the last two digits of
the 2005th power of 7?
B.478. You have three number cards. Each
card has a digit on it that is different from the other two digits. Using
these cards, create all possible 1-, 2-, and 3-digit numbers. The sum of
these numbers is 5635. What are the digits on the cards?
B.479. Ann, Beatrix, Cecilia, Diana, and
Emma are going to the movies where they want to sit in 5 consecutive seats.
However, Ann wants to sit next to Beatrix, and Diana wants to sit next to
Emma, but Cecilia does not want to sit next to Emma. How many different
ways can the girls sit down?
B.480. In a faraway country there are only
3, 5, and 7 rupee coins. How many different ways cab you pay 40 rupee if
you are not allowed to get any money back?
Please, send your solutions to: