222335
1023456789
There are only two smaller 3-digit numbers and both of them have repeated digits.
102
103
The smallest 4-digit number without any repeated digits is 1023, as it starts with the smallest possible digit (1) followed by the next smallest digits (0, 2, 3). The largest 4-digit number without any repeated digits is 9876, which uses the largest digits available in descending order.
1000000000 or, if negative numbers are permitted, then -9999999999
1023456789
The smallest number with no digits repeated would either be zero or one, depending on the set of numbers you want to choose from.
10234567
There are only two smaller 3-digit numbers and both of them have repeated digits.
100 unless negative numbers are permitted: in which case, the answer is -999
10234567
0123456789
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