Question

Write the smallest three digit number with unique digits.

Answer 1

Hint: The question asks us to find the smallest three digit number which we can easily find by listing down the smallest three digit number but as given in the question we also have to simultaneously check if the number obtained is unique, that is no digit in the number are repeated.

Complete step-by-step solution:
Try to start the solution by listing the smallest three digit number as primarily we have to find a three digit number.
So the listing starts by 100,101,102,103… and so on
Now our motto is to not only find the smallest three digit number but it should also be unique.
That is no digit in the number is to be repeated
So we will start checking our list such that no digit is repeated.
100 is rejected as it doesn’t satisfy our second condition i.e. digits are not unique.
Coming to our second number 101, it is also rejected as it also doesn’t contain a unique digit.
Coming to our third number it is to be accepted because it is the smallest number of all where no digits are repeated.
After sorting we get our smallest three digit unique number as 102 which is both smaller and unique.

Note: When given such kinds of questions always try to list down the basic list of numbers. Then try to sort or modify the numbers in respect to the conditions given. This helps is not getting confused with the numbers and helps to get our desired number within a few steps and as formulas can be applied.