What is the smallest 8-digit number having 4 different digits?

Answer 1

4

Answer 2

To make the smallest digit you can, you want to use the smallest numbers you can. Since we need to use 4 different digits, we'll use:0, 1, 2, 3

Now to generate the smallest number, you'll want the lowest digits to be the left most numbers. The exception here is, you don't want to begin a number with 0, so 1 is the next best choice.

A four digit example:

1023 <-- because 0123 doesn't make much sense as a four digit number

The conditions given, are that we only have to use 4 different digits, so using the highest digits once each shall suffice.

10000023

Notice how the higher digits come at the end of the number. That is the key do doing these sorts of problems.

The answer is: 10000023

Bonus:

If each of the four different digits had to be used twice, the answer would be:

10012233, and the number is still ordered with larger digits at the end, with the one still leading because starting with a zero doesn't make sense.