SOLUTION: I am 4 digit number. My thousands digit is thrice as large as my digit in the ones place and half that of my hundreds digit. My tens digit is the smallest single digit possible. W

So we have four blanks to fill in:
_ _ _ _

The ten's digit is 0 because it is the smallest single digit possible.

_ _ 0 _

The only digits that can be thrice another are 0,3,6,and 9, but 0
is out because the thousands digit can't be 0.  So that leaves 3,6,
and 9 for the thousands digit. 

The only one of those that can be half another digit is 3. So the
thousands digit is 3, 

3 _ 0 _

And that 3 is thrice the units digit, making the units digit 1. 

3 _ 0 1

And that 3 is also half the hundreds digit, making the hundreds digit 6.

3 6 0 1

Edwin