WOLFRAM|DEMONSTRATIONS PROJECT

Logic Metapuzzle Generator

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A said: In the set {B} there are an even number of knights.
B said: In the set {A,C} there are an odd number of knights.
C said: In the set {A,B,D} there are an odd number of knights.
Then D said one of the following three statements:
In the set {A,B} there are an even number of knights.
In the set {A,C} there are an odd number of knights.
In the set {A,B} there are an odd number of knights.
Who is a knight and who is a knave?
This Demonstration provides another generator of knights and knaves logic puzzles. These puzzles are about an island in which some natives called "knights" always tell the truth and other natives called "knaves" always lie. Assume that every native is either a knight or a knave.
In the problem there are
n
natives, A, B, C, …, each of whom makes a statement about the number of knights in a set. They know the empty set { } with no knights. Their vocabulary is rather limited; they only talk about even {0, 2, 4, …} and odd {1, 3, 5, …} numbers.
The statement of the last native was not recorded properly, but a logician who had heard the statement was able to infer who was a knight and who was a knave. Can you infer who is a knight and who is a knave?