November Problem Solving

Problem SolvingMP3: Construct viable arguments and critique

the reasoning of others.

A Fraction Problem

A half is one third of it. What is it?

11/1

Number of Numbers

How many different 1-, 2-, or 3-digit whole numbers can be made using the digits 2, 5, and 8?

No digit may be repeated within any one number.

2 5 8

11/2

Fractions and the Flu

You catch the flu, and your

doctor prescribes some

medicine. You are to take

one pill every 2/3 hour. You

have 18 pills to take. How

many hours will the pills

last?

11/5

Percent Problems

You are going to a sporting goods store to buy a pair of tennis shoes and a pair of in-line skates. The original cost of the tennis shoes was $150, but today that pair of tennis shoes is 40% off. The original price of the in-line skates was $200, but today that item is 20% off. What was the percent of discount on the total purchase (assuming no taxes are involved)?

11/6

Twin Primes

Twin primes are a pair of prime numbers such that the lesser

prime number subtracted from the greater prime number is 2.

There are three pairs of twin primes between 100 and 150.

How many pairs of twin primes are there less than 100?

..., 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, ...

11/7

Product of Primes

The product of three prime numbers that

are less than 30 is 1955.

What are the three prime numbers?

11/8

Mystery NumberI am thinking of a special four-digit number:

• All the digits are different.

• The digit in the thousands place is 3 times the digit in the tens place.

• The number is odd.

• The sum of the digits is 27.

What’s my special four-digit number?

11/9

The Winner is...

The winner of a school election is announced after school at 4:00 p.m. One student calls 2 friends before 4:15 p.m., telling the name of the winner. Before 4:30 p.m., those 2 people call 2 more students and tell them the name of the winner. Before 4:45 p.m., each new student who has been notified calls 2 more people, telling them the name of the winner. If this continues and no student is called twice, at what time will 200 students know the name of the winner?

11/13

The Product is Prime?

Find three integers in arithmetic progression

(with equal differences between each number)

whose product is a prime number. (This is

possible.)

11/14

From Perimeter to Area

When a square piece of paper is folded in half vertically, the resulting rectangle has a perimeter of 39 cm. In square centimeters, find the area of the original square sheet of paper.

11/15

The Missing Number

Determine the missing number based on the values in each square.

11/16

Hens and Eggs

If 3 hens lay 4 eggs in 5 days, how

many days will it take a dozen hens

to lay 8 dozen eggs? Please round

your answers to the nearest day (or

egg, if needed).

11/19

Hug a Tree

Several years ago, I planted a 3-foot tree that has grown the same amount each year. At the end of the third year, the tree was 1/5 taller than it was at the end of the second year. The tree is now 18 feet tall. How many years ago did I plant the tree?

11/20

Maximize the Regions

What is the greatest number of

regions you can get if you draw

four straight lines through a

circle? Convince someone that

you found the greatest

number!

11/21

1, 2, 3,...

What three consecutive counting

numbers have a sum that is 20% of

the product of the three numbers?

11/26

Alphanumeric Puzzle

Find the digits that represent the

letters E, F, G, and H to satisfy

the following puzzle. Each letter

represents a different digit.

11/27

There’s Algebra in There!

Complete the table by determining the value of each letter. Explain what rule is used to relate the numbers in the second column (with the heading of y) with those in the first column (with the heading of x).

11/28

Determining Weights

Three boys, Jamal, Hector, and Simon, work together on a farm. They walk into the barn, notice a scale. used to weigh cattle, and decide to weigh themselves. Unfortunately, the scale begins at 100 kg and none of the boys weighs more than 100 kg. They decide to weigh themselves in pairs and found these amounts. Jamal was sure that he weighed the most. What did each boy weigh?

11/29

Mystery Number Puzzle

Find an integer between 100 and 200 such that

each digit is odd and the sum of the cubes of the

digits is equal to the original three-digit number.

11/30