puzzle 049 curious village

Understanding the Puzzle First, let's recall the details of Puzzle 049 from Professor Layton and the Curious Village. The puzzle is titled "The Three Chairs", and it presents the following scenario: Three chairs are placed in a row. Each chair is a different color: one is red, one is blue, and one is green. Three peopleA, B, and Csit in the chairs. Each person is wearing a hat, and each hat is one of the three colors (red, blue, green), but not necessarily matching the chair colors. No person is wearing a hat that is the same color as their chair. Also, no two people are wearing hats of the same color. Person A is sitting in the red chair. Person B is wearing a blue hat. What color is Person C's hat? Breaking Down the Information Let's list out the given information systematically: Chairs and Their Colors: There are three chairs in a row, each a distinct color: red, blue, green. - Chair colors: Red, Blue, Green. People and Their Seating: - Person A is sitting in the red chair. - Persons B and C are sitting in the remaining two chairs (blue and green), but we don't yet know who is in which. Hats and Their Colors: - Each person is wearing a hat that is one of the three colors: red, blue, green. - No person's hat color matches their chair's color. - No two people are wearing hats of the same color (all hat colors are distinct). - Person B is wearing a blue hat. Assigning Variables To make this clearer, let's assign variables: Lets denote the chair colors as follows: - Chair 1: Red (occupied by A) - Chair 2: Blue - Chair 3: Green Persons B and C are in Chair 2 or Chair 3. Hat colors: A's hat: ? B's hat: Blue C's hat: ? Constraints: No person's hat color matches their chair color. - So, if someone is in the red chair, their hat isn't red, etc. All hat colors are distinct. B is wearing a blue hat. Determining Possible Hat Colors First, let's consider Person A: A is in the red chair, so A's hat cannot be red. Possible hat colors for A: blue or green. But B is wearing a blue hat, and all hat colors are distinct, so A cannot also wear blue. Therefore, A's hat must be green. Now, we have: A: red chair, green hat. B: ? chair, blue hat. Now, let's assign chairs to B and C. Possible chair assignments for B and C: B is in blue chair, C is in green chair. Or B is in green chair, C is in blue chair. Let's explore both scenarios. Scenario 1: B is in the blue chair, C is in the green chair. B is in blue chair, wearing blue hat. - But the constraint says no person's hat color matches their chair color. - Here, B's hat is blue and chair is blue This violates the constraint. - Therefore, this scenario is invalid. Scenario 2: B is in the green chair, C is in the blue chair. B is in green chair, wearing blue hat. - Hat (blue) chair (green) Valid. C is in blue chair, hat color? - Possible hat colors: red, blue, green. - Cannot be blue (B is wearing blue). - Cannot be same as chair color (blue), so cannot be blue (already covered). - A is wearing green, B is wearing blue, so C cannot wear green or blue (since all hats are distinct and A has green). - Wait, let's list all hats: - A: green - B: blue - So C must wear the remaining color: red. - Check if red is allowed for C: - C is in blue chair, hat is red. - Does hat color match chair color? No (red blue) Valid. - Also, no duplicate hat colors (A: green, B: blue, C: red) Valid. This scenario satisfies all constraints. Verifying No Other Possibilities Is there any other way to assign chairs to B and C? We've considered: B in blue, C in green invalid (B's hat matches chair). B in green, C in blue valid. No other assignments are possible since chairs are only red (A), blue, and green. Conclusion From the valid scenario: A: red chair, green hat. B: green chair, blue hat. C: blue chair, red hat. Therefore, Person C's hat is red. Final Answer Person C's hat is red.