Ambiguous Question?

Let $n$ be the number of digits in the answer to the question.

For $N < 1000$ , the only multiple answers could be $n =$ 1 vs 2, $n =$ 2 vs 3, or $n =$ 3 vs 4.

For $n =$ 1 vs 2, we have 5 possibilities, $N =$ 5 through 9. (e.g. For $n =$ 7, both 7 and 14 would be correct answers)

For $n =$ 2 vs 3, we have 16 possibilities, $N =$ 34 through 49.

For $n =$ 3 vs 4, we have 84 possibilities, $N =$ 250 through 333.

$5+16+84 = \boxed{105}$