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The problem described in the image is a classic logic puzzle where you need to determine the ages of three daughters based on the given clues. Here’s a step-by-step breakdown of how to solve it:

### Clues:
1. **The product of the three daughters' ages is 36.**
2. **The sum of their ages equals the number of the house.**
3. **There isn't enough information until it’s mentioned that the oldest daughter plays the piano.**

### Step 1: Find all possible combinations of ages that multiply to 36.
Let's consider all the possible integer combinations of ages where the product is 36:

- \( 1 \times 1 \times 36 \) (Sum = 38)
- \( 1 \times 2 \times 18 \) (Sum = 21)
- \( 1 \times 3 \times 12 \) (Sum = 16)
- \( 1 \times 4 \times 9 \) (Sum = 14)
- \( 1 \times 6 \times 6 \) (Sum = 13)
- \( 2 \times 2 \times 9 \) (Sum = 13)
- \( 2 \times 3 \times 6 \) (Sum = 11)
- \( 3 \times 3 \times 4 \) (Sum = 10)

### Step 2: Use the sum to identify the correct combination.
The second clue tells us that the sum of the ages is equal to the number on the house. The fact that Juan couldn’t immediately determine the ages means that the sum must correspond to more than one possible combination of ages.

Looking at the sums, we see that the sum 13 appears twice:
- \( 1 \times 6 \times 6 \) (Sum = 13)
- \( 2 \times 2 \times 9 \) (Sum = 13)

Since Juan initially couldn't determine the ages, the sum of the house number must be 13.

### Step 3: The oldest daughter plays the piano.
The third clue states that the oldest daughter plays the piano. This means there must be a distinct "oldest" daughter.

- In the combination \( 1 \times 6 \times 6 \), there isn't a unique oldest daughter because two daughters are of age 6.
- In the combination \( 2 \times 2 \times 9 \), the oldest daughter is 9.

### Conclusion:
Given these deductions, the ages of Pedro’s daughters must be **2, 2, and 9**.

Would you like more details on this solution or further explanations? 

Here are five related questions for further exploration:

1. How would the solution change if the product of the ages was different?
2. What if there was no information about the oldest daughter? Could you still solve the puzzle?
3. How does the uniqueness of the oldest daughter affect the possible solutions?
4. Can this type of logic puzzle be solved using algebraic methods?
5. What are other classic logic puzzles that use similar reasoning?

**Tip:** When solving logic puzzles, pay attention to every clue provided, as often one small detail can change the entire solution.

Dos amigos, Juan y Pedro, se encuentran después de mucho tiempo. Juan le pregunta a Pedro cómo le va la vida. Pedro le responde que tiene tres hijas y Juan le pregunta qué edades tienen. Pedro le dice que el producto de las tres edades es 36 y que su suma es el número de su casa (la casa de Juan). Juan piensa un rato y le dice que no hay suficiente información para saber las edades de sus hijas, a lo que Pedro responde que la mayor toca el piano. Juan descubre inmediatamente las edades de las hijas de Pedro. ¿Cuáles son las edades de las tres hijas de Pedro?

Discover how to determine the ages of Pedro's three daughters using logic. The product of their ages is 36, and the sum equals the house number. The final clue is that the oldest daughter plays the piano. Suitable for Grades 7-10.

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