ABACUS International Math Competition

for

3rd and 4th graders

October, 1997

A.9. Starting from the 1 in the top left corner and making steps to the right or down, get to the 9 in the bottom right corner so that the sum of the numbers on your way would be 100.

A.10. How would you continue the following number sequences? Why?

a) 1, 1, 2, 3, 5, 8, 13, ...

b) 1, 2, 6, 24, 120, ...

A.11. There are a few chickens and rabbits on a backyard. There are a total of 11 heads and 36 legs. How many chickens are there on the backyard?

A.12. Can you find 4 whole numbers whose sum and product are both odd numbers?

A.13. Find the greatest whole number with all different digits, and 72 as the product of its digits.

A.14. One of my friends turned to be just as many years old in 1995 as the sum of the digits in the year of his birth. What year was he born?

A.15. There are 80 balls in a basket. 35 of them are red, 25 of them are green, 15 of them are yellow, and 5 of them are black. At least how many balls do you have to take out of the basket without looking in order to have:

a) a red

b) a red or black

c) a red and a black

d) two different colors

e) 3 of the same color?

A.16. The following statements can be read on a piece of paper:

1. There is no more than one true statement on this paper. 2. There are no more than two true statements on this paper. 3. There are no more than three true statements on this paper. 4. There are no more than four true statements on this paper. 5. There are no more than five true statements on this paper.

Which statements are true on this paper?

Please, send your solutions by the end of October to:

tdiveki@gcschool.org

Solutions of previous problems

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