Smallest 6-digit number formed by using digits `5, 0, 3, 2, 6, 1` each only once is ______ .

Options

A. `032615`
B. `102356`
C. `102365`
D. `012356`

Answer

To find the smallest 6-digit number formed by using the digits `5, 0, 3, 2, 6, 1` each only once, we can follow these steps:

### Step-by-Step Solution:

1. **List the Digits**: First, we need to list the digits we have: 0, 1, 2, 3, 5, 6.

2. **Sort the Digits**: Next, we arrange these digits in increasing order: 0, 1, 2, 3, 5, 6.

3. **Identify the First Digit**: The first digit of a 6-digit number cannot be 0 (as it would make it a 5-digit number). Therefore, we need to choose the smallest non-zero digit, which is 1.

4. **Construct the Number**: After placing 1 as the first digit, we can now use 0 and the remaining digits to form the smallest number. The next digits in increasing order are 0, 2, 3, 5, and 6.

5. **Arrange the Remaining Digits**: Placing the remaining digits after 1 in increasing order gives us: 0, 2, 3, 5, 6.

6. **Final Number**: Therefore, the smallest 6-digit number formed is 102356.

### Answer:
The smallest 6-digit number formed by using the digits `5, 0, 3, 2, 6, 1` each only once is **102356**.

---