Mr. Math Puzzler was a little tricky about one of his two pizza questions in the July Math Puzzlers.

In Question 4, a lot of the math involved using the familiar pi, radius and squaring. That gives you the area of the pizza. Then, there's some figuring to get the area of a smaller pizza while retaining the "cheesy" flavor of the larger pizza.

Then, you back out the area to go back to pi, radius and squaring. But, the key to the final answer is to then double that radius to get the diameter of the smaller pizza.

That doubling proved to be a stumbling block.

That's an easy mistake to make and that's what makes figuring math so frustrating at times. But, maybe that's part of the fun. If you make a simple mistake like that, it's likely the correct answer will stay with you in the future.

Mr. Math Puzzler is Wayne Hesse, an 8th grade math teacher at Green Park Lutheran School. His August Puzzlers will be his last time with Young Saint Louis.com's math initiative.

His final offerings are straight-forward and have good variety.

YSL.com will be continuing to offer math content. We'll be announcing the new approach during the upcoming school year.

We want to thank Mr. Hesse for his work with YSL.com. We hope our new math initiatives will have the same mixture of fun and math expertise.

To enter the August Math Puzzler competition, just click here.

Remember, kids who get all the August Puzzlers correct will have their names published in the September edition. Also, up to three winners will be awarded $10 Borders gift certificates.

Answers to July Math Puzzlers

1. The 30 students in a class line up in a row. The largest number of consecutive boys in a row is 4. What is the maximum number of boys in the class?

Answer: 24

The explanation: If you have a maximum of four boys in a row before there is a girl, that means there are a total of five kids. Then, you divide 30 by 5 and you know there can be six of those 5-kid groupings. That means you need at least six girls in the class. That leaves 24 boys.

 

2. For how many different two-digit numbers is the tens digit larger than the ones digit?

Answer: 45

The explanation: You should set up a chart. In the 0-9 group, there are zero. In the 10-19 group, there is 1 and in 20-29, there is 2. Going on, 30-39, 3; 40-49, 4; and so on to 90-99, 9. Adding those numbers, you get a total of 45.

 

3. In how many different ways can you receive $20 from your bank if you ask for paper money only? (No $2 bills please.) (Mr. Math Puzzler suggests using a table.)

Answer: 10

The explanation: In a table, you'd have four different denominations, $20, $10, $5 and $1.

	$20	$10	$5	$1
1.	1	-	-	-
2.	-	2	-	-
3.	-	1	2	-
4.	-	1	1	5
5.	-	1	-	10
6.	-	-	4	-
7.	-	-	3	5
8.	-	-	2	10
9.	-	-	1	15
10.	-	-	-	20

 

4. To make a 12-inch pizza, you need 1 1/2 cups of shredded cheese. You have only 1 1/4 cups of cheese. What diameter pizza, to the nearest inch, should you make so that the 1 1/4 cups of cheese will taste as "cheesy" as the 1 1/2 cups on the 12-inch pizza?

Answer: 11 inches

The explanation: First you want to figure the area of a 12" diameter pizza. That's Area = Pi R squared, with the radius being 6". That shows an area of 113.04 square inches. In the second formula, you want to figure the relationship of 1.5 cups of cheese to the 113.04 square inches of the 12-inch pizza to the 1.25 cups of cheese to the smaller area. The area of the smaller pizza is 94.2 square inches. Then, you reverse that using the first formula and you get a radius of 5.48 inches. But, that's the radius and you need to double that for the diameter of the new pizza. Rounding that to the nearest inch, that's an 11 inch pizza.

 

5. How many different kinds of pizza can be ordered if you can top them with any combination of sausage, pepperoni, onions, green peppers, mushrooms and olives? Each topping can be used once on a pizza. (Hint: This is a probability question.) (Note: Cheese isn't listed because all pizza has cheese.)

Answer: 63

The explanation: This calls for combinations. If you got a very large number, you probably were working with permutations, where order of the ingredients would come into play and inflate the possibilities. But, in our problem, with one ingredient, there would be six possibilities. With two ingredients, that would be C times 6 and divided by 2, or 25 possibilities. Using that same formula, three ingredients would have 20 possibilities; four ingredients would have 15 possibilities; five ingredients, 6 possibilities and six ingredients, one possibility. Those numbers total 63 combinations.

 

6. A board game for 2 to 6 players has a deck of cards that always can be divided evenly among all the players. What is the smallest number of cards possible?

Answer: 60

The explanation: In this answer, you're looking for a least common multiple. For 2 players, the prime is 2. For three players, the prime is 3. For four players there are 2 primes of 2. For five players, there a prime of 5. And for six players, there is a prime of both 2 and 3. Then, to find the least number of cards, you multiple the primes of 2 x 3 x 2 x 5 and get 60 cards.