ABACUS International Math Challenge
for
5th and 6th graders
April, 2001
Please, note my new e-mail address
on the bottom of this page!
B.249. Find all those 4-digit even numbers
in which the sum of the digits is 11 and the product of the digits is 20.
B.250. In the following addition table
the 10 letters mean 10 numbers. (For example: G+C=14) Find the numerical
value of each letter.
B.251. Create a trapezoid (but not a square)
by putting together the least possible number of isosceles right triangles.
B.252. Dilbert and Dogbert were enjoying
a lazy afternoon at the office doing nothing so they decided to play number
games. Dilbert said to Dogbert, "I am thinking of an odd number with
three digits. All three digits are different and their sum is 12. The difference
between the first two digits equals the difference between the last two
digits." Can you help Dogbert discover Dilbert's number?
by Jonathan Dornian, Canada
B.253. You have a big 2m x 1.5m x 1.4m
box. Can you fill it up completely (without leaving any air pockets inside)
with 1m x 5dm x 3dm-size boxes, so that none of the smaller boxes is sticking
out of the big box?
B.254. Fill in the blanks of the following
grid with the numbers 1, 2, 3, 4, 5, and 6, so that every row, every column,
and both diagonals contain each of these numbers exactly once.
B.255. Find three numbers out of which
the square of any one of them is the sum of the two other numbers, and the
sum of the three numbers is positive.
B.256. Read the following 5 statements
very carefully:
(A): Statement (B) is true.
(B): No more than one statement is true out of statements (A), (B),
(C), (D), and (E).
(C): All the statements (A), (B), (C), (D), and (E) are true.
(D):
(E):
Statements (D) and (E) are written with a magic ink so that they are
not visible to those who do not tell the truth all the time.
Which ones of the statements (A), (B), (C), (D), and (E) are true?
Please, send your solutions to: