The first digit would have to be 1, the remaining digits, zero.
100,000,000,000
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.
The smallest 10-digit number with no repeated digits is 1023456789. This number starts with 1, the smallest non-zero digit, followed by the remaining digits in ascending order, ensuring all digits from 0 to 9 are used exactly once without repetition.
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.
999,999,999,999
The smallest number with no digits repeated would either be zero or one, depending on the set of numbers you want to choose from.