There are eight houses on Jerry's side of the street. All the house numbers are even numbers from 2 to 16 . Jerry noticed that the sum of the house numbers to the left of his house equals the sum of the house numbers to the right of his house. What is the number of Jerry's house?

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**Step 1. List the House Numbers**

The houses have even numbers from 2 to 16:
$$
2,\ 4,\ 6,\ 8,\ 10,\ 12,\ 14,\ 16
$$

**Step 2. Calculate the Total Sum**

The total sum of all houses is:
$$
S = 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16
$$
We can calculate $$S$$ by pairing or using the formula for an arithmetic series. Notice there are 8 terms, with the first term $$a = 2$$ and the last term $$l = 16$$:
$$
S = \frac{8}{2}(2 + 16) = 4 \times 18 = 72
$$

**Step 3. Set Up the Equation**

Let Jerry's house be numbered $$j$$. The houses to the left of Jerry's house will have a sum $$L$$ and the houses to the right of Jerry’s house will have a sum $$R$$. According to the problem:
$$
L = R
$$
Also, since $$j$$ is not included in either sum:
$$
L + R + j = S
$$
Substitute $$L = R$$:
$$
2L + j = 72 \quad \Longrightarrow \quad L = \frac{72 - j}{2}
$$

**Step 4. Find the Correct House Number**

$$L$$ must be the sum of all house numbers smaller than $$j$$ among the given list. We check the house numbers one by one:

- For $$j = 2$$:
  $$
  L = 0 \quad (\text{no house to the left})
  $$
  Instead, using the formula:
  $$
  \frac{72 - 2}{2} = 35
  $$
  $$0 \neq 35$$.

- For $$j = 4$$:
  $$
  L = 2 \quad (\text{house to left: } 2)
  $$
  Formula gives:
  $$
  \frac{72 - 4}{2} = 34 \quad (2 \neq 34)
  $$

- For $$j = 6$$:
  $$
  L = 2 + 4 = 6
  $$
  Formula gives:
  $$
  \frac{72 - 6}{2} = 33 \quad (6 \neq 33)
  $$

- For $$j = 8$$:
  $$
  L = 2 + 4 + 6 = 12
  $$
  Formula gives:
  $$
  \frac{72 - 8}{2} = 32 \quad (12 \neq 32)
  $$

- For $$j = 10$$:
  $$
  L = 2 + 4 + 6 + 8 = 20
  $$
  Formula gives:
  $$
  \frac{72 - 10}{2} = 31 \quad (20 \neq 31)
  $$

- For $$j = 12$$:
  $$
  L = 2 + 4 + 6 + 8 + 10 = 30
  $$
  Formula gives:
  $$
  \frac{72 - 12}{2} = 30
  $$
  Here, the two values match.

**Step 5. Conclusion**

Since for $$j = 12$$ the condition $$L = \frac{72 - j}{2}$$ holds true, Jerry's house is numbered:
$$
\boxed{12}
$$
Jerry's house number is 12.

There are eight houses on Jerry's side of the street. All the house numbers are even numbers from 2 to 16 . Jerry noticed that the sum of the house numbers to the left of his house equals the sum of the house numbers to the right of his house. What is the number of Jerry's house?

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