ABACUS International Math Challenge
for
3rd and 4th graders
February, 2001
A.233. Using all of them, write the numbers
1, 2, 3, 4, 5, 6, 7, 8 into the fields of the following diagram so that
there are no consecutive numbers in fields with one or two mutual vertices.
A.234. Using every one of the digits 1,
2, 3, 4, 5, 6, 7, 8, and 9 exactly once, find two numbers whose product
is greater than 843 000 000.
A.235. How many 4-digit numbers are there
in which the sum of the digits is 4?
A.236. Find the smallest positive whole
number that is worth the same whether you read it backwards or forwards,
it contains the same digit twice the most, and the sum of its digits is
40.
A.237. From the number 12345678910111213141516171819
delete ten digits so that the remaining 19-digit number is:
a) the greatest possible
b) the smallest possible.
A.238. Out of five consecutive whole numbers,
add the even numbers, and then add the odd numbers. The difference of these
two sums is 36. What are these five numbers?
A.239. Write addition, subtraction, or
multiplication signs between the numbers 1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2
1 on the left hand side of the following equality, so that the equality
is true:
1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1 = 123456
by Mary Panchenko, Santa Clara, California
A.240. Every 6 weeks Mr. Mathews' class
of 20 students has a spelling bee. The spelling bee works like this: all
the students (present that day) line up in one big line. Mr. Mathews has
6 lists, each list contains 20 basic words followed by 7 challenge words.
He goes through each list in order, asking the students one-by-one to spell
the next word, starting with the first student in line, making as many complete
rounds as possible.
One day during line-up Ben, Carl, Lilly and Lucas ran to get particular
spots in the line. They told Mr. Mathews that they wanted those spots because
the people in those spots would not be asked any challenge words that day.
After some pushing and shoving they all got a spot they wanted. By the end
of the bee, each student spelled 9 words that day.
How many students were absent that day and which spots did Ben, Carl,
Lilly and Lucas pick?
by Carl Dawson, New York, New York
Please, send your solutions to: