He said: "I provide you a number S which is the sum of my secret

3 digit number X and 2 two-digit numbers derived from X by erasing one of its digits.

S is a 3 digit number composed of distinct digits. I want you, using no computation aids, just your brains, pen and paper to solve my conundrum.

The sum is 439 - What is my original number?"

Needless to say it was solved in no time, you can treat it as a d1 entry and handle it p&p.

But it inspired the following generalization addressing the perplexus society, rather d3:

There are plenty of 3 digit numbers using 3 distinct digits in the range of 102 to 987 (i. how many?).

Ii. How many, if used as S in the puzzle will provide a valid and unique X?

iii. How many yield: no solution?

iv. How many, if any, 2 or more answers?