Write the smallest 8-digit number having five different digits.

Answer

To find the smallest 8-digit number using five different digits, we can follow these steps:

### Step 1: Identify the digits
We need to choose five different digits. The smallest digits available are 0, 1, 2, 3, and 4.

### Step 2: Determine the placement of digits
Since we are forming an 8-digit number, the first digit cannot be 0 (as it would then be a 7-digit number). Therefore, we will start with the smallest non-zero digit, which is 1.

### Step 3: Fill in the remaining positions
After placing 1 in the first position, we can use the digit 0 in the next positions. However, we need to ensure that we use all five different digits (0, 1, 2, 3, and 4) in our number.

### Step 4: Construct the number
We can place 0 in the second position and then fill the remaining positions with the other digits. To keep the number as small as possible, we can place the remaining digits (2, 3, and 4) in the next available positions.

### Final Arrangement
Thus, the smallest 8-digit number we can form is:
- 1 (first digit)
- 0 (second digit)
- 0 (third digit)
- 0 (fourth digit)
- 0 (fifth digit)
- 2 (sixth digit)
- 3 (seventh digit)
- 4 (eighth digit)

So, the final answer is **10000234**.

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