Spy , Knight, Knave

Logic Level 1

There are three people (Alen , Broad and Cruz), one of whom is a knight, one a knave, and one a spy.

The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth.

  • Alen says: "Cruz is a knave."

  • Broad says: "Alen is a knight."

  • Cruz says: "I am the spy."

Who is the knight, who the knave and who the spy?

Alen is knave, Broad is Knight, Cruz is spy Alen is knight, Broad is spy, Cruz is knave Alen is Spy, Broad is Knave, Cruz is Knight

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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3 solutions

Kenny O.
Sep 14, 2017

As there is only 1 knight in the 3, the knight would not say another person is a knight or he is not a knight, meaning that Broad and Cruz are not knights
this means that Alen is a knight, showing that Cruz is a knave (and Broad a spy)

2 Helpful 1 Interesting 1 Brilliant 0 Confused
Munem Shahriar
Jul 8, 2017

  • Alen is a Knight

  • Broad is a Spy

  • Cruz is a Knave

Broad is not the knight, since if he is, then Alen would also be the knight.

Cruz is not the knight, since his statement would then be a lie.

Therefore Alen is the knight. And Cruz is the knave, and Broad is the spy.

2 Helpful 1 Interesting 1 Brilliant 0 Confused
Saya Suka
Feb 8, 2021

Alen : "Cruz is a knave!"
Broad : "Alen is a knight!"
Cruz : "I am the spy!"

Between Alen and Cruz, one must be telling the truth while the other lies (not necessarily a pair of a knight and a knave, just that their truth values are in opposition). Thus, Cruz is either a spy (a self-claimed truthful spy at that) or a knave (as told by a truthful Alen).
Then, Alen or Broad must be the knight. Since there is only one knight, that sole knight would have to identify himself as one or stated about another truth, since he cannot introduce another knight who didn't exist. With this fact known, we now know that Alen is a Knight, Cruz a knave and Broad a truthful spy.

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