Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.
A pattern of letter Z as `Z`

Answer

To find the rule that gives the number of matchsticks required to make the letter "Z", we can follow these steps:

### Step 1: Identify the number of matchsticks for one "Z"
To create the letter "Z" using matchsticks, we can visualize it as follows:
- The top horizontal line requires 1 matchstick.
- The diagonal line requires 1 matchstick.
- The bottom horizontal line requires 1 matchstick.

So, the total number of matchsticks needed to form one "Z" is:
\[ 1 + 1 + 1 = 3 \]

### Step 2: Establish a variable for the number of "Z"s
Let’s denote the number of "Z"s we want to create as \( n \).

### Step 3: Write the rule using the variable
Since each "Z" requires 3 matchsticks, if we want to create \( n \) "Z"s, the total number of matchsticks required can be expressed as:
\[ \text{Total matchsticks} = 3n \]

### Step 4: Verify the rule with examples
- If \( n = 1 \) (1 "Z"):
\[ 3 \times 1 = 3 \text{ matchsticks} \]
- If \( n = 2 \) (2 "Z"s):
\[ 3 \times 2 = 6 \text{ matchsticks} \]
- If \( n = 3 \) (3 "Z"s):
\[ 3 \times 3 = 9 \text{ matchsticks} \]
- If \( n = 4 \) (4 "Z"s):
\[ 3 \times 4 = 12 \text{ matchsticks} \]

### Conclusion
The rule for the number of matchsticks required to create \( n \) letters "Z" is:
\[ \text{Total matchsticks} = 3n \]