A Strict Digital Sum

The only possible numbers that satisfy the given conditions are:

$\large{1000001} \\ \large{1000010 } \\ \large{1000100 } \\ \large{1001000 } \\ \large{1010000 } \\ \large{1100000 } \\ \large{2000000 } \\$

These numbers are $\boxed{07}$ in number :)

The number must be greater than 1,000,000. Here, to make sum of the digits be 2, another number of 1 must be inserted in place of any single zero, which can be done in six ways, and the last way is 2,000,000, hence there are 7 methods.

The numbers are:

1000001

1000010

1000100

1001000

1010000

1100000

and

2000000