Write all 3-digit numbers using the digits 1, 3, 5 taking each digit only once.

Answer

To find all the 3-digit numbers using the digits 1, 3, and 5, while ensuring that each digit is used only once, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Digits**: The digits we have are 1, 3, and 5.

2. **Determine the Number of Digits**: Since we need to create 3-digit numbers, we will use all three digits.

3. **List All Possible Arrangements**: We can arrange the digits in different orders. The total number of arrangements of three different digits can be calculated using the factorial of the number of digits, which is 3! (3 factorial).

\[ 3! = 3 \times 2 \times 1 = 6 \]

4. **Generate the Arrangements**:
- Start with 1:
- 135
- 153
- Start with 3:
- 315
- 351
- Start with 5:
- 513
- 531

5. **List All Unique 3-Digit Numbers**: From the arrangements above, we can list the unique 3-digit numbers:
- 135
- 153
- 315
- 351
- 513
- 531

### Final Answer:
The 3-digit numbers that can be formed using the digits 1, 3, and 5, each used only once, are:
- 135
- 153
- 315
- 351
- 513
- 531