Math and Arithmetic

# What is the smallest 5 digit number having only 3 different digits?

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

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.