Knight Knave and Spy Logic Puzzle: Multiple Paths to Solution

Submitted by Atanu Chaudhuri on Sun, 31/03/2024 - 19:30

Analyze Statements in the Knight Knave and Spy Logic Puzzle: Use Your Deductive Reasoning

Challenge yourself with the Knight Knave and Spy logic puzzle. How many ways can you solve this liar, truth-teller, and the random-answerer puzzle?

The Liar, Truth-teller, Random-answerer Logic Puzzle: Simple Version

One of Arun, Barun and Chris 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 tell the truth or lie. Arun says, "Chris is a knave." Barun says, "Arun is a knight." Chris says, "I am the spy." Who is the knight, who the knave and who the spy?

How many different ways can you reason out the answer?

Time for you for the answer and the many ways to reach the solution is: 30 minutes.

Don't just stop after getting one solution. Ask yourself, "Can there be any other way of reasoning to find the same answer or a second answer?" And disover unique reasoning methods of solving this cute deductive reasoning puzzle.

The more you ask such questions, you will discover new possibilities in every new problem, and it will strengthen your inherent logic analysis skill.

Liar, Truth-teller, Random-answerer Logic Puzzle: Solution by Step-by-Step Logical Reasoning

First reasoning path: Start analyzing the statement of Chris first:

We will analyze the statement of Chris first, as he identifies himself in his statement. Chances are: we'll be able to find a self-contradiction in his statement.

Looking for a contradiction in a chain of logic analysis is an important trick to tackle reasoning puzzles. This method usually succeeds in producing a breakthrough.

When facing a statement-based logic puzzle, always look for contradiction. This is the potent Contradiction Search technique in solving statement-based liar truth-teller puzzles.

Let us analyze the statement of Chris and see what conclusions we can arrive at.

Chris says, "I am the spy."

First logical reasoning: The spy can tell either the truth or lie. If Chris is a spy and is telling the truth, he is a spy. If he is lying, he cannot be the Knight who always tells the truth.

Conclusion: Chris can either be the spy or the knave, but not the knight.

To verify these two possibilities, the most suitable method is to look for a statement that refers to Chris. This is link search technique by far the most potent technique in unraveling the twists in logic reasoning puzzles. Arun refers to Chris in his statement, "Chris is a knave."

Second logical reasoning: If Chris indeed is the spy, Arun must be lying by his statement, "Chris is a knave." One possibility for identifying Arun is left: he must be the knave (who always lies) and so, Barun must be the knight.

But, Barun cannot be the knight as he identifies Arun as the knight by his statement, "Arun is the knight." This is the contradiction we were looking for.

In a chain of reasoning, there can either be a contradiction or a confirmation at the end, both with complete certainty and no ambiguity.

At the end of this reasoning chain, we land onto a contradiction: Implication: the original assumption of Chris telling the truth must be false. He must be lying. And if he is lying, he cannot be the spy (because of self-contradiction) or the knight.

Final conclusion: Chris cannot be the spy, and must be the knave.

Identifying Arun and Barun is left.

Third logical reasoning: Arun says, "Chris is a knave." And it turned out to be true. So, Arun is telling the truth and might be the spy or the knight. If Arun is the spy, Barun must be the knight. But, Barun says, "Arun is the knight", the second contradiction. Implication: Arun cannot be the spy, he must indeed be the knight, and in this case, Barun, the spy is telling the truth.

Answer: Arun is the knight, Barun the spy and Chris the knave.

Tricky? Not so, if you apply your logical reasoning skills along with link search technique that is based on, what we call, extended common sense.

Now we will start analyzing a different statement first.

Can it discover another solution or confirm our first solution! Let us see.

Second reasoning path: Analyze Barun's statement first

Barun's statement has the advantage of tying up two of them as well as bringing in the knight who always tells the truth. Identifying the knight or the Knave is easier by contradiction, but identifying the random-answerer is more tricky.

Barun says, "Arun is the knight."

If it is true, he can only be the occasionally truth-telling spy (he cannot be the knight as there would then be two knights, a contradiction).
As Chris is claiming to the spy, he is lying and be the knave. with Arun as the knight. All statements confirming each other, if Barun is the spy and is telling the truth.
Answer in this case: Arun the knight, Barun the spy and Chris the knave.

But what if Arun lied!

A golden rule in logical reasoning analysis is,

Explore all the possibilities. Never leave a loose end hanging alone in the reasoning possibilities.

So, we need to consider Barun lying.

If Barun lied, he can either be the spy or the knave, not the knight. Also, Arun with his statement, "Chris is a knave" must not be the knight and also lied, leaving Chris to be the knight which he is not by his statement, "I am the spy." Again, we land onto a contradiction: Implication: the original assumption that Barun lied is false.
So, Barun must be telling the truth as a spy.
Answer in this path of reasoning: Arun the knight, Barun the spy and Chris the knave. Same as before, only the path to the solution is different.

Third reasoning path: Analyze statement of Arun first

We leave it for you.

Different way of logic analysis gives a good feel about the quick way and the longer way to reach the solution. The exercise also makes your grip on logic analysis stronger. This in general is the strength of the many ways technique of problem solving. It makes you a better problem-solver.