ABACUS International Math Challenge

for

5th and 6th graders

October, 1999

B.137. The product of three positive whole numbers is 30, and their sum is divisible by 4. What are these three numbers?

B.138. Write the numbers 2, 5, 11, and 17 into the empty squares so that the equality is true:

(((+1)+1)+1)=1995

B.139. A college student had 31 exams in 5 years.Every year he had more exams than in the previous year. In his 5th year he had three times as many exams as in his first year. How many exams did he have in the fourth year?

B.140. What do we have more of: the ababab type 6-digit numbers that are divisible by 3, or the abaaba type 6-digit numbers that are divisible by 7?

B.141. In the following multiplication () same letters mean the same digits, different letters mean different digits. What could the value of the product be?

DADA=EDDA

B.142. There are 5 people sitting around a round table, and one after the other they all make the same following statement: "Both of my neighbors at this table are liars." You know that the liars always lie, and those who are not liars are always telling the truth. At this table everybody knows about everybody else whether they are liars or not. How many liars are sitting at this table?

B.143. My grandfather, when he was over 65 but younger than 90, said: "All my children have the same number of children and siblings, and I am just as old as the total number of my children and grandchildren." How old was my grandfather then?

B.144. There is a 10 meter long line of children marching forward one behind another. Their teacher from the end of the line walked to the beginning of the line, and when she got there, she turned around and walked back to the end of the line. She walked three times as fast as the children. How far did the children walk during the teacher's "trip"?

Please, send your solutions to:

tdiveki@gcschool.org

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