Let four digits be1000a+100b+10c+d.

Then it is1000d+100c+10b+a after inversion.

Explain that a and d are not equal to zero.

The difference between them is1000 (a-d)+100 (b-c)+10 (c-b)+(d-a).

So d=a+ 1.

c=b

So the smallest number is 1002.