101
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As the number is odd it must end in an odd digit; the odd digits are 1, 3, 5, 7, 9 and the smallest is 1 which is the sum of 1 and 0. Thus the smallest 7-digit number which meets your criteria is 1,001,001
1
4638
No. 1000 has 4 digits and is the smallest 4-digit number. The smallest 3-digit number is 100.
The smallest is 1111 if repeats are allowed. If not, it is 1235.