Catching the spy

Logic Level 2

You are on a FBI mission and you crashed your plane and find yourself on an uncharted island. On this island lies (pun intended) knights, knaves and one spy. Knights always tell the truth, knaves always lie, and the spy can tell either.

You have narrowed down your suspects to 3 people, Alex, Bart and Carson. There is ONLY one knight, one knave, and one spy between the three.

Alex: "Carson is a knave!"

Bart: "Alex is a knight!"

Carson: "I am the spy!"

Who is the spy?

Image credit: https://www.washingtonblade.com/2015/01/14/threes-crowd/

Alex Carson Bart

Jonathan Tse by Jonathan Tse , 20, Hong Kong

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3 solutions

Marc Tudosoiu
Jun 15, 2019

Just looking from the sentences we can claim that Alex is a knight because the other two statements aren't something that a knight would say. If Bart was to be a knight it wouldn't be possible for him to tell the truth and say that there is another knight because there is only one knight. And Carson can't be a knight either because then he would lie about being a spy. Therefore if Alex is a knight and says that Carson is a knave, Bart is the only option left for a spy!!!!

1 Helpful 1 Interesting 1 Brilliant 0 Confused

I think you mean "the other two statements aren't something that a SOLE knight would say".

Saya Suka - 1 month, 2 weeks ago
Saya Suka
Feb 8, 2021

Alex : "Carson is a knave!"
Bart : "Alex is a knight!"
Carson : "I am the spy!"

Between Alex and Carson, 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, Carson is either a spy (a self-claimed truthful spy at that) or a knave (as told by a truthful Alex).

Then, Alex or Bart 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 Alex is a Knight, Carson a knave and Bart a truthful spy.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

By that conversation alone without anymore conditions than there are 2 spies at most amongst the three, we may have :
1) Sir Alex the Knight, Carson the knave and Bart the truthful spy, OR
2) Alex the knave, Carson the truthful spy and Bart the lying spy, OR
3) Alex the lying spy, Carson the truthful spy and Bart the knave, OR
4) Sir Alex the Knight, Carson the knave and Sir Bart the Knight (for a no-spy solution), OR
5) Alex the truthful spy, Carson the knave and Bart the lying spy, OR
6) Alex the truthful spy, Carson the knave and Bart the knave, OR
7) Alex the knave, Carson the truthful spy and Bart the knave.

Saya Suka - 4 months ago
Jonathan Tse
Jun 9, 2019

First of all, we can see that Carson cannot be a knight, as he can't have two occupations( A knight and a spy).

If Carson was the spy, then the rest won't work out. The only two occupations left are the knight and knave. If Bart was the knave, then Alex must be the knight. But if Bart was telling a false statement, then Alex would have to be a knave. If Bart was a knight, then Alex couldn't be one too.

Therefore, Carson must be a knave.

Bart couldn't be the knight, because if Bart was a knight, then Alex couldn't be one too.

Therefore, by elimination, Bart must be the spy.

0 Helpful 0 Interesting 0 Brilliant 2 Confused

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