ABACUS International Math Challenge

for

7th and 8th graders

October, 1999

C.137. Are there three such prime numbers that have a sum of 1234 and a product of 87654321?

C.138. The sum of 49 positive whole numbers is 999. How high could the greatest common factor of these numbers be?

C.139. Laurie picked three consecutive numbers. Then she took two of them in every possible combination and multiplied them. Could the sum of these products be 3 000 000?

C.140. Two bicycle clubs organize a tour together. At the meeting in the morning members great each other with a handshake. Everybody shakes hands with everybody once. There were a total of 231 handshakes but 119 of them happened between members of the same club. How many members came from each club?

C.141. Find all those 3-digit numbers that are divisible by 7, and they give the same remainder when divided by either 4, 6, 8, or 9.

C.142. Susie was wondering: "Isn't it interesting that my mother's age is half of the sum of my father's and my age; my father and my mother together are 100 years old; both my father's and my mother's age is prime?"

How old is Susie?

C.143. In the following multiplication () same letters mean the same digits, different letters mean different digits. What could the value of the product be?

BIGBIG=LOTBIG

C.144. Seven dwarves are sitting around a round table with a mug in front of each with some milk in it. (Some mugs might be empty.) There is a total of a half a liter of milk in the mugs. One dwarf stood up and distributed his milk evenly among the other dwarves. Then, one by one, everybody towards his right did the same thing. After the seventh dwarf distributed his milk, everybody ended up having the same amount of milk than what they started with originally. How much milk was in each mug?

Please, send your solutions to:

tdiveki@gcschool.org

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