ABACUS International Math Challenge
for
5th and 6th graders
October, 2002
B.329. One day 12 children from a class
went to see a movie. On another day 9 children from the same class went
to see a puppet show. 10 children from the class did not go to either program.
Minimum and maximum how many children could there be in the class?
B.330. If Hilary is a boy then he is younger
than John. If Hilary is 13 years old then Hilary is a girl. If Hilary is
not 13 years old then Hilary is at least as old as John. Is Hilary a boy
or a girl?
B.331. A no more than 5-digit number has
to following interesting properties: if you read it backwards you get the
same number; if you turn it up-side-down, you get the same number; if you
put a mirror next to the number on its side, you will see the original number
in the mirror. Find all these numbers.
B.332. A group of students went on a school
trip. They got to this beautiful water fountain, where the teacher made
them stand around the circular base at an equal distance from one to the
next child. Then the teacher counted them and told them to remember their
numbers. In the middle of the fountain there was a column from which the
water was shooting up. The only student child number 15 could not see from
the column was child number 49. How many children are there in the group?
B.333. Find all those 3-digit numbers that
are divisible by 6, and the sum of their digits is 24.
B.334. A positive whole number has exactly
8 positive divisors, including 35 and 77. Find this number.
B.335. Four athletes, Anna, Bill, Cecilia,
and David, are sitting around a small, circular table. There is a swimmer,
an ice skater, a skier, and a runner among them. The swimmer is sitting
on the left of Anna, the skier is sitting across from Bill, Cecilia and
David are sitting next to each other, and there is a girl sitting on the
left of the ice skater. What is the name of the runner?
B.336. A flee keeps on jumping along a
straight line. First it jumps 1 meter, then 2 meters, then 4 meters, and
it keeps on doubling the distance of its jumps. The flee may pick before
every jump whether it wants to jump right or left on the straight line.
Can it get back to its starting point? What if it can jump parallel or perpendicular
to this straight line?
Please, send your solutions to: