1. Ms. Sarahvanan asked the class to see if they could find the sum of the first 50 odd numbers. As everyone settled down to their addition, Terry ran to her and said, "The sum is 2,500." Ms. Arroyo thought, "Lucky guess," and gave him the task of finding the sum of the first 75 odd numbers. Within 20 seconds, Terry was back with the correct answer of 5,625.

How does Terry find the sum so quickly? (20 Marks)

2. You have a piece of paper, 10cm by 10cm. Area = 100cm2. For some reason, you need a square piece of paper with an area of 50cm2. Using the paper you have, what's an easy way of getting the new square?(30 Marks)

3. When I went to the store, I purchased four items. The following shows the cost of three of the items:

$1.50$3.00$4.00

The line to the checkout was pretty long, so to quench my boredom I started playing with my pocket calculator while waiting.

I found out, to my surprise, that the four prices of the four items I purchased added to the same number as I got when I multiplied the four prices together.

What was the price of the fourth item?(40 Marks)

4. Arrange the numbers 1 through 9 on a tic tac toe board such that the numbers in each row, column, and diagonal add up to 15. (25 Marks)

5. A man wanted to get into his work building, but he had forgotten his code. However, he did remember five clues. These are what those clues were:

The fifth number plus the third number equals fourteen.

The fourth number is one more than the second number.

The first number is one less than twice the second number.

The second number plus the third number equals ten.

The sum of all five numbers is 30.

What were the five numbers and in what order?(40 Marks)

6. If 125207 is "Hi", and 031993121212 is "Dude", then 125207031993121212 is "Hi Dude".

Then what is 799717777010909230151693122001983?(20 Marks)

7. What is the number pattern?31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334, 365(20 Marks)

8. Your objective is to buy exactly 100 farm animals with exactly 100 dollars. You must buy at least 1 of each animal. You may need some paper!

The Costs:Cows: $10 eachPigs: $ 3 eachChickens: $0.50 each(40 Marks)

9. The year 1978 has an unusual property. When you add the 19 to the 78, the total is the same as the middle two digits (97). What will be the next year to have this same property?(30 Marks)

10. Fill the eight spaces below with numbers from 1 to 8. No number that comes before or after any other number should be placed in an adjacent space, either horizontally, vertically or diagonally.

(For Example 2 should not be next to the number 1 or the number 3)(20 Marks)

11. Question :(30 Marks)