What is the Smallest 3-Digit Number with Unique Digits?

The smallest 3-digit number with unique digits is 102, as a 3-digit number must have three digits, the first of which cannot be zero. To ensure all digits are unique, no digit can repeat. By arranging the smallest digits (0, 1, 2) in ascending order while adhering to these rules, we get 102.

Complete Answer: 

What Does “Unique Digits” Mean?

A number has unique digits if no digit is repeated. For example, 112 is not valid because the digit 1 is repeated, while 102 is valid because all its digits (1, 0, 2) are different.

Why Can’t the First Digit Be 0?

A 3-digit number begins at 100. If the first digit is 0, the number would become a 2-digit number, such as 012, which does not meet the requirement.

What is the smallest 3-digit number?

• The smallest non-zero digit is 1, so it becomes the first digit.
• The next smallest digits after 1 are 0 and 2. Using these ensures the digits are as small as possible while remaining unique.
• To form the smallest number, arrange them in ascending order: 102.

Interesting Facts About 3-Digit Numbers with Unique Digits

• The largest 3-digit number with unique digits is 987, using the digits 9, 8, and 7.
• There are a total of 648 unique 3-digit numbers. This is calculated as: 

9×9×8=648

The first digit has 9 choices (1–9), the second has 9 choices (0–9 excluding the first digit), and the third has 8 choices (excluding the first two digits).

The smallest 3-digit number with unique digits is 102. Once you know this concept, not only it will strengthen your grasp of basic number theory but also enhance your problem-solving skills in combinatorics and logic.