A logic problem by Sofia Kwan
Logic
Level
1
Alex says " me, Luce and Anya are knights." Luce says: if I am a knight Anya is one too... Hendrick says: I am a knave and Anya is a knave.
what you know: there are at least 2 knights.
Luce is the only knight
none of them are knaves
Luce and Alex are knaves and Anya and Hendrick are knights
Hendrick is a knave
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Lets start with Hendrick:
Suppose he is a knight. Then, he always tells the truth, hence, according to his statement, he is a knave. That is a contradiction, thus we conclude that Hendrick is a knave and this is a correct option for the problem. At the same time the option " Luce and Alex are knaves and Anya and Hendrick are knights " is wrong because of the last part of this statement. Moreover, the option " none of them are knaves " is also wrong.
Since Hendrick is a knave, his statement is false, but the lie is not what he says about himself, so he lies about Anya. This, tells us that Anya is a knight. Consequently, the option " Luce is the only knight " is wrong. Having checked for consistency, we conclude that the (only) correct answer is Hendrick is a knave .