ABACUS International Math Challenge
for
5th and 6th graders
December, 1999
B.153. Pair-up every positive whole number
with another number that is equal to the original number plus the sum of
its digits. (For example: 17 is paired-up with 25.) There are such lonely
numbers that you cannot pair-up with any number. What is the 10th smallest
lonely number?
B.154. Replace the x's in the following
multiplication with digits so it is a correct multiplication. (Some x's
mean different digits than others.)
B.155. Convert the following infinite repeating
hexadecimal (base 16) fraction into a decimal fraction:
0.1999DECDECDEC...
Csaba Daday, Romania
B.156. Find all those two-digit numbers
that when increased by 4, the sum of their digits become half of what they
were.
B.157. Find all those three-digit numbers
that when increased by 3, the sum of their digits become a third of what
they were.
B.158. A maid's yearly salary was $12 and
coat. However, when she quit after 7 months, she received $5 and the coat.
What was the value of the coat?
B.159. How many triangles are there with
whole-number-long sides and a perimeter of 9?
B.160. In a league the teams received a
total of 420 points. You got 2 points for a victory, 1 points for a tie,
and 0 points for a loss. How many teams were there in the league if every
team played every team twice?
Please, send your solutions to: