One idea would be to take the first 8 digits 0,1,2,3,4,5,6, and 7 and order them such that the biggest number is the first digit then the next biggest etc. This should do it, but then we would start with a 0 and that is really a 7 digit number. So let's just make the zero second. 10234567 Can you find a smaller one? If you don't use 0, then you have 1,2,3,4,5,6,7,8 and the number would be 12345678 but that is bigger. There is the issue of negative numbers which I have ignored on purpose! And, do we consider decimals like 1.0234567?
1023456789
102
103
There are only two smaller 3-digit numbers and both of them have repeated digits.
none
1023456789
10234567
0123456789
10234567
Since there are only five different digits, a 6-digit number can only be generated if a digit can be repeated. If digits can be repeated, the smallest 6-digit number is 111111.
102
103
100,000,000,000
The smallest number with no digits repeated would either be zero or one, depending on the set of numbers you want to choose from.
Oh, what a happy little question! To find the smallest 6-digit number with no repeated digits, we start by using the digits 1-9 in ascending order. So, the smallest 6-digit number with no repeated digits is 123,456. Just imagine all the beautiful possibilities that number holds!
1000000000 or, if negative numbers are permitted, then -9999999999
The first digit would have to be 1, the remaining digits, zero.