Math Problems

When a number is multiplied by itself, the answer is a perfect square. 

For example, 25 is a perfect square because 5 x 5 is 25. 

In how many ways can the number 1764 be written as the product (multiply) of two perfect squares?

Solution

1764 can be written as a product of two perfect squares in three ways.  

• 4 x 441
• 9 x 196
• 36 x 49

(It can also be written as a product of three perfect squares 4 x 9 x 49)

Which is a better deal, one round pizza that is 18 inches in diameter for $15 or two round pizzas that are both 12 inches in diameter for $15?

Solution 

The 18 inch diameter pizza is a better deal.  The area of a circle can be found by the formula A=pi x radius x radius.  The area of the top of the 18 inch diameter pizza is about 254 square inches.  The area of the top of one 12 inch diameter pizza is about 113 square inches so two of them would have a top area of about 226 square inches. 

If you roll two six-sided fair dice are you more likely to get an even result if you add the top numbers or if you multiply them?

Solution

You are more likely to get an even result if you multiply the dice.  If you add them the probability of getting an even number is ½.  If you multiply the numbers, the probability of getting an even number is ¾.

Suppose there was one of six prizes inside your favourite box of cereal. 

How many boxes of cereal would you expect to have to buy to get all six prizes?

Simulate this with a six-sided die.  Roll the die and keep track of how many rolls it takes to get all 6 numbers. 

Repeat the experiment several times. 

Approximate the answer to this question by finding the mean (arithmetic average) of all of your results

Where on this number line would you place the number 1 billion?

Solution