1. I’m thinking of a number…
A Question…
I’m thinking of a number…
Objective: Chapter 3 - Eliminate Possibilities

2. I’m thinking of a number…
A Question…
I’m thinking of a number…
It’s 54!
Objective: Chapter 3 - Eliminate Possibilities

3. Example
Three brothers each arranged to spend an evening with a woman that he had never met before. Each wanted to show off how suave and debonair he could be, so each formed a plan.
By coincidence, each brother decided to buy a box of candy at the same store, and each bought tickets at the same ticket outlet.
When it came time to leave, each brother grabbed the wrong candy box and ticket envelope. None of them took the candy or the tickets that belonged to him. Each took the tickets of one brother and the candy of the other. Andy didn’t have Marty’s candy…you figure out the rest.
Objective: Chapter 3 - Eliminate Possibilities

4. Another Example
Penny’s favorite coin is the dime. Since we last saw Penny, she has spent some of her dimes and has acquired some more. She doesn’t know how many she has now, but she knows she has fewer than 100. One day she was arranging them on her desk in different ways. She found that when she put them into piles of 2, there was 1 left over. When she put them into piles of 3, again there was 1 left over. The same thing happened when she put them into piles of 4. She then tried putting them into piles of 5 and found that there were none left over. How many dimes does Penny have? (There is more than one correct answer).
Objective: Chapter 3 - Eliminate Possibilities

5. Proof by contradiction – Indirect Proof
Another Methodology
Proof by contradiction – Indirect Proof
We make an assumption and then look for an occasion where it is not true.
Objective: Chapter 3 - Eliminate Possibilities

6. Example
Jim tells lies on Fridays, Saturdays, and Sundays. He tells the truth on all other days. Freda tells lies on Tuesdays, Wednesdays, and Thursdays. She tells the truth on all other days. If they both say, “Yesterday I lied,” then what day is it today?
Objective: Chapter 3 - Eliminate Possibilities

7. Cryptarithms
Emil and Olive live on a farm with their father, Gordon. One day Emil asked his father, “Dad, what happened to that cat we used to have?” Olive overheard this and said, “Yeah, and we used to have a horse too.” Gordon replied, “That tomcat and that old nag were no use. I traded them for our new goat.”
Objective: Chapter 3 - Eliminate Possibilities

8. Cryptarithms…Continued
Emil said, “Hey, that sounds like a good cryptarithmetic problem. Come on Olive, let’s see if we can solve it. Each letter stands for a different digit, 0 through 9. No two letters stand for the same digit.
T O M
N A G
G O A T
Objective: Chapter 3 - Eliminate Possibilities

9. Another Example
Seymour sells his Sausage and Meatball Combo to 2 Fast Stop stores and one Circle B store. After an accident, he can’t remember which streets the stores are on. What he does know is that the streets are numbers from 1st Street up to 154th Street, and he remembered that the two Fast Stop stores were on streets whose numbers added up to 50. He also remembered that the Circle B store was two streets away from one of the Fast Stop stores. And he remembered that he called the Sausage and Meatball Combo his “prime” favorite because all three stores were on prim-numbered streets. He didn’t have enough information yet…
Objective: Chapter 3 - Eliminate Possibilities

10. We Continue
He called his friend Gus and Gus could remember only the last digit of the product of the numbers of the streets the stores were on. Find the street numbers.
Objective: Chapter 3 - Eliminate Possibilities

11. Homework
Page 68, 1-8 all
Objective: Chapter 3 - Eliminate Possibilities