ABACUS International Math Challenge
for
7th and 8th graders
January, 2001
C.233. Find a pattern, and write the appropriate
signs into the fields of the last square.
C.234. Find all those 5-digit positive
whole numbers that are square and cube numbers also.
C.235. How many 4-digit numbers are there
in which the sum of the digits is 5?
C.236. Find the integers a, b, and c for
which ab=144, bc=240, and ac=60. ( ab means the product of a and b.)
C.237. Find a 6-digit number that gets
6 times greater when you move its last 3 digits to the front of the number
without changing the order of these three digits.
C.238. How many 3-digit numbers are there
in which the digits are such that if you create all the different 3-digit
numbers from them, and you add these numbers, the sum is divisible by 111?
C.239. How many different ways can you
place 2 different coins on the square fields of an 8x8 chess board so that
their fields do not share a side or a vertex?
C.240. Last year a class organized three
school trips. 70% of the class went on the first trip, 80% on the second
trip, and 90% on the third trip. 12 students attended all 3 trips, everybody
else went twice. How many students are there in this class?
Please, send your solutions to: