Write all 3-digit numbers using 2, 3, 4 taking each digit only once.

Answer

To solve the problem of writing all 3-digit numbers using the digits 2, 3, and 4, with each digit used only once, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Digits**: The digits we have are 2, 3, and 4.

2. **Understand the Requirement**: We need to form 3-digit numbers using each of these digits exactly once. This means we cannot repeat any digit in a number.

3. **List the Possible Combinations**: We can arrange the digits in different ways to form different numbers. The total number of arrangements of 3 digits is calculated using the factorial of the number of digits, which is 3! (3 factorial).

- Calculation:
\[ 3! = 3 \times 2 \times 1 = 6 \]

4. **Generate the Numbers**:
- Start with 2:
- 234
- 243
- Start with 3:
- 324
- 342
- Start with 4:
- 423
- 432

5. **List All the Unique 3-Digit Numbers**:
- The unique 3-digit numbers formed are:
- 234
- 243
- 324
- 342
- 423
- 432

### Final Answer:
The 3-digit numbers using the digits 2, 3, and 4, each used only once, are:
- 234
- 243
- 324
- 342
- 423
- 432