Jumat, 24 Februari 2012

Olympiad Math Exercise

For the 1st and 2nd graders
1.     Bay street has between 1 and 15 houses, numbered 1,2,3, and so on. Mr. Sulivan lives in one of the houses. The sum of all the house numbers less than his equals the sum of all the house numbers greater than his. How many houses are there on Bay street?
2.     David has 4 cages of hamster. The second cage has ½ as many hamster as the first. The third cage has ½ as many hamster as the second. The fourth cage has ½ as many hamster as the third. What is the smallest number of hamsters David can have?

For the 3rd and 4th graders
1.     A large alligator has a body and tail that is 5 times as long as its head. From the tip of its nose to the tip of its tail the giant alligator is 300 decimeters long. How long is its head?
2.     In a 4th grade class 11 children know how to swim, 6 of these children are boys. There are 14 boys all together in the class. 7 girls in the class do not know how to swim. How many students are there in this class?
3.     If a life is worth 2 zebras or 3 bears, and a monkey is worth a bear and a zebra, what is the value of each of these animals expressed with the value of each of the other animals?
4.     Suppose you stack 45 blocks to make a pyramid with one block on the top, 2 blocks in the next row, and so on. How many blocks are in the bottom row? How many rows are there?
5.     Mr. Sigman used 36 fence posts to build a fence around his square back yard. He used an equal number of posts on each side of his yard. How many posts were on each side?
6.     Arthur had $ 10 more than Burt, so he gave Burt half of his money. Then Burt had more money than Arthur, so he gave Arthur $ 4. Then they both had $ 13. How much money did each person start with?

For the 5th and 6th graders
1.     The mass of a jar is 1340 grams when it is full of water, and 720 grams when it is half way. What is the mass of the jar when it is empty?
2.     On a column with a rectangular base there are 3 different kinds of sides with the areas of 28, 32 and 56 square centimeters. What are dimensions of the column?
3.     If a cowboy bought 15 more cows he would have twice as much as if he sold 5 of them. How many cows does he have now?
4.     If 20 people go to a party and they all shake hands with one another, how many handshakes will there be?
5.     A book has 300 pages numbered 1,2,3 and so on. How many times does the number 1 appear?
6.     The sum of two numbers is 180, the difference between them is 80. What are the numbers?
For the 7th and 8th graders
1.     If it takes an escalator 1 minute to get you down to the platform in a subway/metro station, and it takes you 30 seconds to run down the stairs, how long does it take you to run down to the platform on the escalator that is
a.     Going down?
b.     Going up?
2.     Imagine that you had a tape measure that you could stretch around the earth at the equator. The tape would fit so tightly that nothing could fit between the tape measure and the surface of the earth, not even a thin blade steak knife.
Now, imagine that you increased the length of the tape measure by only 1 cm, i.e., you increased the circumference by 1 cm. Would that give you enough room so that now you could slide the steak knife between the tape measure and the earth?
How much do you have to increase the circumference by in order for a 150 cm tall person to be able to walk under the tape stretched out evenly above the surface of the earth?
3.     Sara rolled 2 dice and made the following statements about it:
1.     Both numbers are greater than 4
2.     One number is even and the other one is odd
3.     Their sum is even
The second statement is false, but the first one is true. Could the third statement be true? What could Sara roll?