Knights and knaves

Two people, Red and Blue, stand before you. Red says, “We are both knaves.” What are they really?

• Red is knave, Blue is knight.

• Red is knight, Blue is knave.

• Both of them are knights.

• Both of them are knaves.

Two people again. Red says, “We are both the same type of people,” and Blue says, “We are each different types of people.” What are their identities?

• Blue is knave, Red is knight.

• Blue is knight, Red is knave.

• Both of them are knights.

• Both of them are knaves.

To complicate matters, a new island is discovered, with a third type of inhabitant: spies, who can either tell the truth or lie. You encounter three people, one of each, but you don’t know which is which. Red says, “I am a knight.” Blue says, “Red is telling the truth.” Green says, “I am the spy.” Who is what?

• Red is spy, Blue is knight, Green is knave.

• Red is knight, Blue is spy, Green is knave.

• Red is knave, Blue is spy, Green is knight.

• Red is knight, Blue is knave, Green is spy.

Now add the wrinkle of language difficulties. On yet another island, the inhabitants are all either knights or knaves, and though they understand English, they will not utter the words Yes and No. They use “Ja” and “Da,” but we do not know which means Yes and which means No. Upon encountering an inhabitant of this island, you ask, “Does Ja mean Yes?” He answers, “Ja.” Have you learned what Ja means? Have you learned whether the person is a knight or a knave?

• You have learned the meaning of Ja and Da, but you do not know that the person is a knight or a knave.

• You have not learned the meaning of Ja and Da, but you do know that the person is a knight.

• You have not learned the meaning of Ja and Da, but you do know that the person is a knave.

On a certain island, there are only two types of islanders:

knights, who always tell the truth, and

knaves, who always lie.

You meet two islanders named Aditya and Bowie. Aditya said: Bowie is a knight and I am a knight.

Bowie said: Aditya is a knave or I am a knave.

What types of islanders are Aditya and Bowie?

• Aditya is a knight, Bowie is a knight.

• Aditya is a knave, Bowie is a knave.

• Aditya is a knight, Bowie is a knave.

• Aditya is a knave, Bowie is a knight.

On the same island, you find three friends named Channing, Daija, and Eira.

Channing said: Exactly two of us are knights.

Daija said: Eira and myself are knights.

Eira said: Channing or Daija is a knave.

What type (knight or knave) is Channing?

• Channing must be a knight.

• Channing must be a knave.

• Channing's type is unknown without further information.

You come across two more friends named Fiadh and Greg, but only Fiadh says anything: "If I am a knight, Greg is a knave."

What type is Greg?

• A knight.

• A knave.

• There isn't enough information to be certain.

Finally, just as you are about to leave the island, you find a group of four islanders named Kade, Lovelace, Maxwell, and Nelly, and again you ask what types they are.

Kade says: Lovelace is a knight or I am a knight.

Lovelace says: Maxwell is a knight or I am a knight.

Maxwell says: Nelly is a knight or I am a knight.

Nelly says: Kade is a knight or I am a knight.

Given you know that at least one of them is a knave, exactly how many are knaves?

• 1

• 2

• 3

• 4