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### Section 1.3

Problem Solving

Steps to world problem solving process

- Understand the Problem
- Devise a plan
- Carry out the plan
- Look back
- MAKE SURE YOU ANSWER THE QUESTION

Understand the problem

- Understand?
- Enough info

Devise a plan

- Guess and test
- Look for pattern
- Use algebra
- Make it simple

Carry out the plan

- Implement
- Don’t be afraid to start over

Look back

- Correct solution?

Answer the question

- Check to see if you answered the right question

Problem 1

- Place the digits 1,2,3,4,5, and 6 in the circles below so that the sum of the three numbers on each side is 12.

Problem 2

- What is the sum of the first n consecutive odd numbers?
- For example
- 1=1
- 1+3= 4
- 1+3+5= 9
- 1+3+5+7=16
- 1+3+5+7+9= 25
- 1+3+5+7+9+11= 36

- Predict the first 16 odd numbers…
- =256
- So the answer will be

Problem 3

- There are 20 people at the meeting. If each person shakes hands with every person (except himself) in the room only once, how many handshakes will there be?
- What if there were 2 people? 3? 4?
- 2=1 shakes
- 3=3 shakes
- 4=6 shakes
- 5=10 shakes
- n=n(n-1)/2
- 20=190

Problem 4

- A merchant has a basket of oranges, and sells half of them to the first person and then gives him one more for good measure. He then sells half the remaining oranges to the second person and gives him an extra orange for good measure. A third person buys exactly half the remaining oranges and the vendor gives him one more for good measure. Finally the merchant eats the last orange. How many oranges were originally in the basket?
- 22 oranges

Problem 6

- How many ways can the letter A, B, and C be arranged?
- 6 ways

Example: Drawing a Sketch

An array of nine dots is arranged in a 3 x 3 square as shown below. Join the dots with exactly four straight lines segments. You are not allowed to pick up your pencil from the paper and may not trace over a segment that has already been drawn.

Example: Using Common Sense

Two currently minted United States coins together have a total value of $0.30. One is not a quarter. What are the two coins?

Solution

This involves a “catch.” The two coins are a quarter and a nickel. Note that one of the coins is not a quarter, it is a nickel.

Example: Guessing and Checking

Find a positive natural number that satisfies the equation below.

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