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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.
100,000,000,000
102
103
The smallest number with no digits repeated would either be zero or one, depending on the set of numbers you want to choose from.
1000000000 or, if negative numbers are permitted, then -9999999999
The first digit would have to be 1, the remaining digits, zero.
5
There are only two smaller 3-digit numbers and both of them have repeated digits.