Crossroad Logic Puzzle Explanation

This question is a classic logic puzzle where we need to identify the truthful statement among multiple conflicting claims, knowing that only one person is telling the truth. We have three residents, A, B, and C, providing directions to a traveller at a crossroad.

Understanding the Statements

Here are the statements made by each resident:

• A says: "turn left"
• B says: "do not turn left" (This means turn right or go straight)
• C says: "go straight"

We are told that exactly one of these three residents is truthful.

Analyzing Possible Scenarios (Who is Truthful?)

Let's examine each possibility for who might be the truthful one and see if it leads to a consistent outcome.

Case 1: Assume A is Truthful

If A is telling the truth, then the direction is left.

• A is truthful: Direction is left.
• B must be lying: B says "do not turn left". If B is lying, the truth is the opposite, which is "turn left". This matches A's statement.
• C must be lying: C says "go straight". If C is lying, the truth is the opposite, which is "not go straight". Since the direction is left (as per A), it is indeed not straight.

This scenario is consistent: If A is truthful (left), then B lies (truth is left) and C lies (truth is not straight). This works. So, the direction could be left.

Case 2: Assume B is Truthful

If B is telling the truth, then the direction is not left. This means the direction is either right or straight.

• B is truthful: Direction is not left (either right or straight).
• A must be lying: A says "turn left". If A is lying, the truth is the opposite, which is "not turn left". This matches B's statement.
• C must be lying: C says "go straight". If C is lying, the truth is the opposite, which is "not go straight".

Combining B's truth ("not left", meaning right or straight) and C's lie ("not straight"), the only remaining possibility is that the direction is right.

This scenario is also consistent: If B is truthful (not left, i.e., right), then A lies (truth is not left) and C lies (truth is not straight). This works. So, the direction could be right.

Case 3: Assume C is Truthful

If C is telling the truth, then the direction is straight.

• C is truthful: Direction is straight.
• A must be lying: A says "turn left". If A is lying, the truth is the opposite, which is "not turn left". This is consistent with the direction being straight.
• B must be lying: B says "do not turn left". If B is lying, the truth is the opposite, which is "turn left".

This scenario leads to a contradiction: If C is truthful, the direction is straight. But if B is lying (as required if C is truthful), the direction must be left. The direction cannot be both straight and left at the same time. Therefore, this scenario is inconsistent. C cannot be the truthful one.

Conclusion for the Traveller

Our analysis shows that there are two possibilities where only one person is truthful:

• Possibility 1: A is truthful, B and C are lying. The direction is left.
• Possibility 2: B is truthful, A and C are lying. The direction is right.

Since both scenarios are consistent with the condition that only one person is truthful, and the traveller knows only one person is truthful but doesn't know who, the traveller cannot definitively determine whether the correct direction is left or right. They can rule out 'straight', but are left with two possibilities.

Therefore, the traveller will not be able to decide between going left or right.