What is the smallest 3-digit number with unique digits?

Hint: We need to find the smallest 3-digit number so we fill the first search with the number which has 3 digits in it and considers the smallest one but there is one more condition that the 3-digit number must have all the 3 digits unique. So, we will search for that 3-digit number which is smallest and no digits get repeated in that number.

Complete step-by-step answer: The main objective is to find the smallest 3-digit number with unique digits.
We will first write the numbers which have 3-digits in it and look for the smallest 3-digit number.
Thus, we get,
\[100,101,102,103,.....\]
So, we can easily get the smallest 3-digit number from the above list.
Thus, the smallest 3-digit number is 100.
Next, we need to find the number which has all the unique digits in it.
As we can see in number 100, the digit 0 is repeating twice so, the number 100 is not considered.
Next, we have number 101, in which 1 is repeating twice hence, the number 101 is also not a unique 3-digit number.
Next, we will consider the number 102 which has no digit on repeat and has all the 3-digits unique.
Thus, 102 is the smallest 3-digit number with unique digits.

Note: We can make a list of the numbers which has 3 digits in it and check for the first number in the list which will give us the smallest 3-digit number. For the uniqueness, we have checked whether any digit is repeating in the number or not.