ABACUS International Math Challenge
for
5th and 6th graders
January, 2005
B.465. Find two square numbers with the
difference of 
.
by Michael Schubert, Germany
B.466. In a family three boys have at least
one younger sibling and two boys have at least one older sibling. Two girls
have at least one older sibling and one girl has at least one younger sibling.
There are no twins in this family. How many children are there in this family,
and in which order could the boys and girls be born?
B.467. Timea is putting her building blocks
on her two-arm balance. (Blocks with different colors have different weights.)
First she puts a red and a blue on one side and a green and a yellow on
the other side, and they are in balance. Then she switches the blue and
the green, and this way the yellow and the blue together are heavier than
the red and the green. Finally, she finds that the green and the blue together
are heavier than the red and the yellow. What color block is the heaviest?
B.468. On each bank of a river stands King
Arthur and Sir Robin. Both of them has a lock with a matching key, but the
two locks and their keys are different. One of the men has a box with two
pairs of metal bands on it which can be locked by one lock on each pair
of bands. (Of course, you can lock to box by using only one of the two pairs,
also.) King Arthur wants to send some gold coins to Sir Robin. There is
a carrier on the river who transports everything but people, but he steals
everything that is not locked (even an open empty box). Could the king still
send the gold to Sir Robin? (Notice that the box could be with either one
of the two men originally.)
B.469. The vertices of the gray rhombuses
are the midpoints of the sides of the square and the sixths points of the
diagonals of the square. How big is the gray area if the side of the square
is 21 cm?
B.470. Let the letters of the word ABACUS
mean number digits. (Same letters mean the same digit.) Therefore, the word
means a 6-digit number. What number is it if you know that:
A+B+C=18
AxCxU=48
SxUxB=378
B.471. Numbers that are the same when read
backwards are called palindrome numbers. Find all those palindrome numbers
between 10 and 1000 in which the sum of the digits is the same as the product
of the digits.
B.472. You have four perfect dice, and
you roll them all at once. How many different ways can the sum of the numbers
rolled be 20? (Two rolls are identical if you get the same four numbers.)
Please, send your solutions to: