The Smallest 4-Digit Numbers with Different Digits

To find the smallest 4-digit numbers with different digits, we need to consider the following factors:

1. Understanding 4-Digit Numbers
A 4-digit number is a number that has four digits, with the leftmost digit being non-zero. The range of 4-digit numbers starts from 1000 (inclusive) and goes up to 9999 (inclusive).

2. Different Digits
For a number to have different digits, each digit in the number must be unique. In other words, no two digits in the number can be the same.

3. Finding the Smallest 4-Digit Numbers
To find the smallest 4-digit numbers with different digits, we can start with the smallest digit and incrementally increase each digit while ensuring no repetition.

4. Solution
To construct the smallest 4-digit number with different digits, we can follow these steps:

1. Start with the digit 1 as the leftmost digit, as it is the smallest non-zero digit.
2. For the second digit, choose the smallest digit greater than 1, which is 2.
3. For the third digit, choose the smallest digit greater than both 1 and 2, which is 3.
4. Finally, for the fourth digit, choose the smallest digit greater than 1, 2, and 3, which is 4.

Combining these digits, we get the smallest 4-digit number with different digits, which is 1234.

5. Conclusion
The smallest 4-digit number with different digits is 1234. This number satisfies the given conditions of having four digits and each digit being unique.

1023 is the smallest 4 digit no. with different digits.