ABACUS International Math Challenge
for
5th and 6th graders
March, 2001
B.241. How many 4-digit numbers are there
in which the product of the first digit and the last digit is a cube number,
and the product of the second digit and the third digit is the fourth power
of a number?
B.242. How many different ways can Julie
read the name of her favorite cat, Maffia, if she is allowed to make one
step at a time only to the right or down:
B.243. Delete a few digits from the 17-digit
number 82 077 875 072 562 386 so that you get the greatest possible number
that is divisible by 36.
B.244. The captain of the pirates comes
home after 6 years of prison, and says: "I was 5 times older than my
son when I started my prison term, but now I am only 3 times as old as he
is. When my son gets twice as old as he is now, I will be twice as old as
him." How old was the captain when his son was born?
B.245. There are small and big birds in
a pet store for sale. The big birds are twice as expensive as the small
ones. A lady comes in and buys 5 big and 3 small birds. If she bought 3
big and 5 small birds she would have had to pay $20 less. How much does
each kind of bird cost?
B.246. The teacher wrote a whole number,
less than 50 000, on the board. The first student said that it is divisible
by 2, the second student said that it is divisible by 3, ..., the 12th student
said that it is divisible by 13. Except for two consecutive students, everybody
was right. What number was on the board?
B.247. A book contains at least 30, and
the most 3000 pages. Every page is numbered and the numbering starts with
1, of course. For the numbering of the last few pages, 23 digits were used.
How many pages are there in the book? Find all the possibilities.
B.248. How many different ways can you
distribute 6 different books to 4 people. (It is possible that some of these
people do not receive any book.)
Please, send your solutions to: