ABACUS International Math Challenge
for
7th and 8th graders
September, 2000
C.193. Draw the biggest square inside and
the smallest square outside of a circle. What is the ratio of the areas
of these two squares?
C.194. Find all those fractions whose denominator
is less than 20, and the value of the fraction is between 23/113 and 28/113.
C.195. How many such 3-digit numbers are
there where the sum of the digits is 15, and the number is divisible by
15?
C.196. What is the smallest multiple of
36 that contains only the digits 5 and 0 in its form in base 10?
C.197. In a math test you have to solve
30 problems. You get 5 points for every correct answer, zero points for
an incorrect answer, and you get 1 point for every unanswered problem. How
many different total points can you possibly get on this test?
C.198. Three people, Mr. Black, Mr. Gray,
and Mr. White met on the street.
"Did you notice that we all wear black, gray, and white, but nobody
wears the color of his name?"- asked Mr. Black.
"That is really true!" - said the man in white.
Can you tell the color of each man's dress?
C.199. You roll three dice. The product
of the three numbers is 24. What could the sum of these three numbers be?
C.200. How many such 5-digit numbers are
there containing only the digits 1, 2, and 3, but every one of these?
Please, send your solutions to: