State if the result is always odd or always even:
One even and two odd numbers are added

Answer

To determine whether the result of adding one even number and two odd numbers is always odd or always even, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Types of Numbers**:
- An **even number** is any integer that can be divided by 2 without a remainder (e.g., 0, 2, 4, 6, 8, etc.).
- An **odd number** is any integer that cannot be divided by 2 evenly (e.g., 1, 3, 5, 7, 9, etc.).

2. **Identify the Numbers**:
- Let’s denote the even number as \( E \) and the two odd numbers as \( O_1 \) and \( O_2 \).

3. **Add the Numbers**:
- The expression for adding these numbers is:
\[ E + O_1 + O_2 \]

4. **Use Properties of Even and Odd Numbers**:
- The sum of two odd numbers is always even. This can be shown as:
\[ O_1 + O_2 = \text{even} \]
- Now, when we add an even number to this even result:
\[ E + \text{(even)} = \text{even} \]

5. **Conclusion**:
- Therefore, the sum of one even number and two odd numbers is always even.

### Example Verification:
- **Example 1**: Let \( E = 4 \), \( O_1 = 7 \), and \( O_2 = 9 \):
\[ 4 + 7 + 9 = 20 \quad (\text{even}) \]

- **Example 2**: Let \( E = 10 \), \( O_1 = 21 \), and \( O_2 = 31 \):
\[ 10 + 21 + 31 = 62 \quad (\text{even}) \]

### Final Answer:
The result of adding one even number and two odd numbers is **always even**.

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