ABACUS International Math Challenge
for
5th and 6th graders
November, 2001
B.273. Using a balance, we determined the
following facts: 5 little cubes are just as heavy as 7 cylinders; 9 cylinders
are just as heavy as 3 big cubes; 6 balls are just as heavy as 2 big cubes.
Furthermore, 4 balls have the same mass as 100 g of sugar. What is the mass
of one little cube?
B.274. You have to cook a particular pasta
for exactly 8 minutes. There are two kinds of sand-clocks in the kitchen:
a 3-minute clock and a 7-minute clock. The sand flows down in them with
a constant speed, but there is no scale on them, so you can tell how much
time was spent only when all the sand went down in the clocks. How can we
cook this pasta for exactly 8 minutes using these clocks?
B.275. A girl and a boy are walking in
the park. The one with black hair says: "I am a boy." The blond
says: "I am a girl." We know for sure that somebody is not telling
the truth. Which one is the girl, and which one is the boy?
B.276. Find three integers with a sum of
zero and a product of 12.
B.277. A regular triangle and a regular
hexagon have the same perimeter. The area of the triangle is 2 units. What
is the area of the hexagon?
B.278. What is the remainder when you divide
by 6?
B.279. Find two positive prime numbers,
such that their sum and their difference are positive prime numbers, also.
B.280. Write down the positive whole numbers
from 1 to 100 directly one after the other. From the number 123456789101112...99100
you got this way, pull out ten digits so that the remaining number is the
greatest possible. What digits did you pull out?
Please, send your solutions to: