ABACUS International Math Competition

for

3rd and 4th graders

September, 1997

A.1. In order to get the greatest 3-digit number, how many times do you have to add the greatest 2-digit number to the greatest 1-digit number?

A.2. Is there such a 4-digit number in which every digit is even, none of them is zero, the first and the last digit is the same, and the sum of the first two digits is twice the sum of the last two digits?

A.3. A mother distributes a certain number of apples between her 3 children in such a way that Paula gets half of the apples and two more apples, Tom gets half of the rest of the apples and two more apples, and Andrew gets half of the remaining apples and two more apples. One more apple is still left over. How many apples did the mother have originally?

A.4. Is it possible to pick the + and - signs in such a way that you would get a true equality?

A.5. Is it possible to pick the + and - signs in such a way that you would get a true equality?

A.6. You have to hang 12 light bulbs from the ceiling in such a way that they should be in 6 straight lines, 4 light bulbs on each straight line. How can you make such an arrangement? Give examples for such an arrangement.

A.7. There are 70 balls in a basket. 20 of them are red, 20 of them are green, 20 of them are yellow, and some of the remaining 10 are black and the rest of them are white. At least how many balls do you have to take out of the basket without looking in order to have 10 of the same color?

A.8. The following statements can be read on a piece of paper:

1. There is exactly one false statement on this paper. 2. There are exactly two false statements on this paper. 3. There are exactly three false statements on this paper. 4. There are exactly four false statements on this paper. 5. There are exactly five false statements on this paper.

Which statements are true on this paper?

Please, send your solutions to:

tdiveki@gcschool.org

Solutions of previous problems

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