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Use this problem heuristics to solve the given problems. (Use at least 2 problem heuristics)

Let's break down the problem and apply some problem-solving heuristics:

### Problem Understanding:
Anna is using matchsticks to create a row of houses, and we need to determine how many matchsticks are required for a row of 25 houses. We are also asked if a box of 100 matchsticks will be enough for this, and then to represent the number of matchsticks needed for **n** houses.

### Heuristics 1: **Look for a pattern**
First, observe how the matchsticks are used in the diagram for a small number of houses:

- Each individual house consists of 6 matchsticks (4 for the base and sides, and 2 for the roof).
- However, adjacent houses share one side. This shared side reduces the total number of matchsticks required for every house after the first one.

Let's consider:
- For 1 house, you need 6 matchsticks.
- For 2 houses, you need 6 (first house) + 5 (since one side is shared) = 11 matchsticks.
- For 3 houses, you need 11 + 5 = 16 matchsticks.

Thus, the pattern is that each new house after the first adds 5 matchsticks (since one side is shared).

### General formula:
- For 1 house: \( 6 \) matchsticks.
- For \( n \) houses: The total number of matchsticks is:
  \[
  \text{Total matchsticks} = 6 + 5(n - 1) = 5n + 1
  \]

### Heuristics 2: **Work backwards**
Now let's apply this formula to 25 houses:
\[
\text{Total matchsticks} = 5(25) + 1 = 125 + 1 = 126
\]

### Answer the questions:
1. **How many matchsticks does she need for 25 houses?**
   She will need 126 matchsticks.
   
2. **Is a box of 100 matchsticks enough for the houses?**
   No, 100 matchsticks are not enough because she needs 126 matchsticks.

3. **How would you represent the number of matchsticks for \( n \) houses?**
   The general formula is:
   \[
   \text{Total matchsticks} = 5n + 1
   \]

### Summary of Heuristics:
1. **Look for a pattern**: Observing the pattern of matchstick usage helped create a formula for any number of houses.
2. **Work backwards**: Applying the formula to check how many matchsticks are needed for specific numbers of houses ensures that we can generalize and solve for any value of \( n \).

### Do you have any questions or want further details?

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Here are 5 relative questions that expand on the problem:
1. How many matchsticks would be required for a row of 50 houses?
2. If you had 200 matchsticks, how many houses could you build?
3. How could you adjust the design to use fewer matchsticks per house?
4. What if each house required an additional matchstick for decoration? How would this affect the formula?
5. Can you think of other mathematical patterns or problems that follow a similar structure?

#### Tip:
When trying to solve a problem with repeated elements or patterns, always look for parts that remain constant and parts that change. This helps in forming general rules or equations.

Anna is making a design that looks like a row of houses for her project in Home Economics. How many matchsticks does she need to make a row of 25 houses? Is a box of matches containing 100 pieces enough? Determine the number of matchsticks Ana needs to make a row of n houses.

Determine how many matchsticks are required for a row of 25 houses using an arithmetic pattern. This problem teaches key concepts in pattern recognition and algebra, suitable for students in Grades 5-7.

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