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Knights and Knaves question?
On a remote island there live Knights and Knaves. Knights always tell the truth and Knaves always lie.
You meet two people on the island—A and B.
A says: “Exactly one of us is a Knight.”
B says: “I and A are not the same”
From their statements, determine who is a knight and who is a knave.
A possible answer is that there is no solution. I am leaning towards that answer.
4 Answers
- PaulLv 75 years ago
They are both Knaves.
1. Assume both statements are true, if both are true then both are knights but both claim that they can't both be knights which leads to a contradiction proving our assumption false.
2. Assume A is the knight and B is the knave. If that is correct A's statement would hold up but B's statement is true which is incompatible with the assumption he is a knave.
3. Assume A is a knave and B is a knight. In this case A's statement would be true which is incompatible with our assumption he is a knave.
This leads us to the only alternative which is :
4. Assume both are knaves. This would make A's statement a lie which is compatible with our assumption. It would also make B's statement a lie which is also compatible with our assumption.
- Anonymous5 years ago
Both Knaves, you're a Knight
- PinkgreenLv 75 years ago
Ans. Both A & B are knaves.
Explanation:
If A lies, then what he means is
"both of us are not the knight"
If B lies, then what he means is
"A & I are the same"
=>both A & B are knaves.
