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Homework Assignment Puzzles

The following problems are adapted from their numbered equivalents in Raymond Smullyan's What Is the Name of This Book? The Riddle of Dracula and Other Logical Puzzles (Prentice-Hall, 1978).  Look here for the solutions.

1. It is Saturday afternoon. As you walk down the beach, you meet 3 residents: Tom, Dick and Harry. You know that none are Normals. You ask Tom, "Are you a Knight or a Knave?" He answers, but you cannot make out what he said; so you ask Dick, "What did he say?" Dick responds, "Tom said that he is a Knave." At this point, Harry says, "Don't believe Dick, he is lying." What are Dick and Harry? (Smullyan's #26)
2. It is Saturday afternoon. As you walk down the beach, you meet 3 residents: Tom, Dick and Harry. You know that none are Normals. You ask Tom, "How many Knights are among you?" He answers, but you cannot make out what he said; so you ask Dick, "What did he say?" Dick responds, "He said that one of us is a Knight." At this point, Harry says, "Don't believe Dick, he is lying." What are Dick and Harry? (Smullyan's #27)
3. You meet two residents of the island; Tom and Henry. Neither of them is a Normal. Tom makes this statement, "At least one of us is a Knave." What is each one? (Smullyan's #28)
4. One evening you sit down to dinner with two residents: Susan and Ralph. You know that neither of them is a Normal. Susan says, "Either I am a Knave, or Ralph is a Knight." What are Susan and Ralph? (Smullyan's #29)
5. One evening as you are out for a stroll, you walk by a doorway labeled "No Normals allowed." You hear three voices from within. Curious, you listen and hear the following. Voice one: "All of us are Knaves." Voice two: "Exactly one of us is a Knight." What are the three people inside? (Smullyan's #31)
6. As you are walking on the island, you meet two of the inhabitants, Tim and Grace. You know that neither of them is a Normal. Tim says, "I am a Knave, but Grace isn't." What are Tim and Grace? (Smullyan's #33)
7. As a contestant on the island's only TV quiz show, you face 3 residents: Tommy, Babette and Cathy. You are told that 1 is a Knight, 1 a Knave, and 1 a Normal. Tommy says, "I am a Normal." Babette says, "That is true." Cathy says, "I am not a Normal." Your job is to prove with certainty what each is. (Smullyan's #39)
8. You are at the airport ready to leave the island and fly home. Before being allowed on the plane, you must pass one final test. You are introduced to two residents, Carly and Earl. Carly says, "Earl is a Knight." Earl says, "Carly is not a Knight." One is telling the truth, but is not a Knight. Who is it? (Smullyan's #40)
9. It turns out that on one part of the island there is a rule that Normals can only marry Normals, and Knights and Knaves can only marry each other. One day as you are walking in this part of the island, you meet Mr. and Mrs. Jones. Mr. Jones says, "My wife is not a Normal." Mrs. Jones says, "My husband is not a Normal." What are Mr. and Mrs. Jones? (Smullyan's #44)
10. It turns out that on one part of the island there is a rule that Normals can only marry Normals, and Knights and Knaves can only marry each other. One day as you are walking in this part of the island, you meet Mr. and Mrs. Jones. Mr. Jones says, "My wife is a Normal." Mrs. Jones says, "My husband is a Normal." What are Mr. and Mrs. Jones? (Smullyan's #45)

If you need an assignment sheet in which to place each puzzle, here is a suggestion.

On the island of Knights, Knaves and Normals there are three types of people: Knights, who always tell the truth; Knaves, who always lie; and Normals, who sometimes lie and sometimes tell the truth.  Additionally we know the following about what makes statements true or false:

• In multipart statements connected with OR, all parts must be false for the statement to be false.
• In multipart statements connected explicitly or implicitly with AND, all parts must be true to make the statement true.

<Puzzle goes here.>

Instructions

1. Review the three step logical problem solving procedure we worked with in class.
2. Following that procedure step by step, prepare a rough draft of your solution to the puzzle above.
3. Proofread and correct your rough draft for spelling, punctuation, clarity, conciseness, capitalization, and complete sentences.
4. Prepare a final draft to submit at the start of our next class. Head your final draft with your name, the class name, and the due date. Keep a copy of your final draft and this assignment sheet to use during the oral report your group will present sometime during the next few class periods.
5. When we have finished all oral reports based on this assignment, you will take a test with a puzzle similar to the ones we'll discuss. I will give you a written puzzle, and you will have the period to write out your step by step solution for it. You should do well if you do 3 things between now and the test date. (1) Focus your full attention on the class discussions.  (2) Participate thoughtfully and cooperatively in them. (3) Take good notes to review before the test. As you take your notes, remember that you are trying to develop an understanding of the process, not memorize other people's solutions.