puzzle 41 curious village

Puzzle 41: The Three Daughters from Professor Layton and the Curious Village is a classic age-based logic puzzle. Here's how to solve it: Problem Recap: A man has three daughters. The product of their ages is 36, and the sum of their ages is equal to the house number across the street. The professor then mentions that the eldest daughter plays piano, which is a key clue. What are the daughters' ages? Solution: List all possible age combinations where the product is 36 (including all possible orderings for sums): - (1, 1, 36) Sum = 38 - (1, 2, 18) Sum = 21 - (1, 3, 12) Sum = 16 - (1, 4, 9) Sum = 14 - (1, 6, 6) Sum = 13 - (2, 2, 9) Sum = 13 - (2, 3, 6) Sum = 11 - (3, 3, 4) Sum = 10 Analyze the sums: - If the house number were unique (e.g., 10, 11, etc.), the professor wouldnt need the piano clue. But since he does, the sum must be non-unique (i.e., appearing twice in the list). - Only sum = 13 appears twice: - (1, 6, 6) - (2, 2, 9) Apply the piano clue ("eldest daughter"): - This implies there is one eldest daughter (no twins among the oldest). - (1, 6, 6) would mean two eldest daughters (both age 6), which contradicts the clue. - (2, 2, 9) has a single eldest daughter (age 9). Answer: The daughters are 2, 2, and 9 years old. Let me know if you'd like further clarification!