ABACUS International Math Challenge
for
3rd and 4th graders
March, 2001
A.241. Sally was bored. She picked up a
piece of paper and cut it into 10 pieces. Then she picked up one of these
pieces and cut it into 10 pieces. She repeated this activity for a while.
When she got bored of doing this also, she stood up. Her younger brother
counted all the pieces and said: "You made 2001 pieces of paper."
Soon Sally responded: "You are wrong."
Who was right?
A.242. Using all the digits 1, 2, 3, 4,
5, 6, 7, 8, and 9 once and only once, write down three 3-digit numbers whose
product is greater than 610 000 000.
A.243. Alice and Mr. Rabbit are on their
way to a very important meeting taking place at 5 o'clock, and they did
not want to be late. Mr. Rabbit is wearing a watch and knows exactly how
many minutes before 5 o'clock it is. Alice, however, has no watch and,
as they are walking, she asks Mr. Rabbit what time it is. Mr. Rabbit is
a clever rabbit who loves number puzzles and therefore, he refuses to give
Alice a straightforward answer. Rather, he tells Alice that 40 minutes ago
it was four times as many minutes past 2 o'clock. Using Mr. Rabbit's clues,
help Alice to figure what time it is now.
by Patrick Dornian
A.244. Using mathematical symbols (but
not additional digits), make the following false statement true:
44+55=38
(Crossing the "=" sign is not acceptable.)
A.245. Using 3 planes, cut a cube into
8 identical parts.
A.246. Using 4 planes, cut a cube into
8 identical parts.
A.247. Sleepy has an assignment of sending
some of his 6 partners to the mine every day for the first 6 days of the
week so that any two of these teams have exactly one mutual member. Is this
possible?
A.248. It turned out that in the first
half of the year in the 4th grade there were 15, 11, 8, 7, and 5 children
who received at least 1, at least 2, at least 3, at least 4, and at least
5 A+'s (the highest grade) respectively, and nobody received more than 5
A+'s. How many A+'s in total were given out in the first half of the year
in the 4th grade?
Please, send your solutions to: