The following logic puzzle is taken from Raymond Smullyan's What is the Name of This Book? Formulate the puzzle as a set of con- straints for a 0-1 program. Solve your program to find the solution to the puzzle. Suppose you are visiting a forest in which every inhabitant is either a knight or a knave. Knights always tell the truth and knaves always lie. In addition some of the inhabitants are werewolves and have the annoying habit of sometimes turning into wolves at night and devouring people. A werewolf can be either a knight or a knave. You are interviewing three inhabitants, A, B, and C, and it is known that exactly one of them is a werewolf. They make the following state- ments: A: I am a werewolf. B: I am a werewolf. C: At most one of us is a knight. Give a complete classification of A B and C (ie. which are knights

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The following logic puzzle is taken from Raymond Smullyan's
What is the Name of This Book? Formulate the puzzle as a set of con-
straints for a 0-1 program. Solve your program to find the solution to
the puzzle.
Suppose you are visiting a forest in which every inhabitant is either a
knight or a knave. Knights always tell the truth and knaves always
lie. In addition some of the inhabitants are werewolves and have the
annoying habit of sometimes turning into wolves at night and devouring
people. A werewolf can be either a knight or a knave.
You are interviewing three inhabitants, A, B, and C, and it is known
that exactly one of them is a werewolf. They make the following state-
ments:
A: I am a werewolf.
B: I am a werewolf.
C: At most one of us is a knight.
Give a complete classification of A, B and C (i.e., which are knights,
which are knaves, which are werewolves).
Hint: Let
1 if inhabitant j is a knight
k;
otherwise
and
1
if inhabitant j is a werewolf
0 otherwise
Transcribed Image Text:The following logic puzzle is taken from Raymond Smullyan's What is the Name of This Book? Formulate the puzzle as a set of con- straints for a 0-1 program. Solve your program to find the solution to the puzzle. Suppose you are visiting a forest in which every inhabitant is either a knight or a knave. Knights always tell the truth and knaves always lie. In addition some of the inhabitants are werewolves and have the annoying habit of sometimes turning into wolves at night and devouring people. A werewolf can be either a knight or a knave. You are interviewing three inhabitants, A, B, and C, and it is known that exactly one of them is a werewolf. They make the following state- ments: A: I am a werewolf. B: I am a werewolf. C: At most one of us is a knight. Give a complete classification of A, B and C (i.e., which are knights, which are knaves, which are werewolves). Hint: Let 1 if inhabitant j is a knight k; otherwise and 1 if inhabitant j is a werewolf 0 otherwise
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