Who am I? number puzzles, step by step

"I am a four-digit number.

The question

What number am I?

Cross out everything the clues rule out

1000to9999→9000

still standing:9000

9000→4500

4500→100

100→7

7→1

8060

8150

8240

8330

8420

8510

8600

Nothing is given except statements, and the first thing to fix is how much room there is to search: a four-digit number runs from 1000 to 9999, so there are 9000 of them and 4 clues to get down to one.
Do not try to guess a number and check it against the clues — that is 9000 guesses in the worst case. Take the clues one at a time instead, and keep only the numbers still standing after each. The count going down is the working.
First clue: The ones digit is even. That leaves 4500 of the 9000, roughly halving it.
Clue 2: The thousands digit is 8 more than the ones digit. That leaves 100 of the 4500, which is most of them gone.
Clue 3: Its four digits add up to 14. That leaves 7 of the 100, which is most of them gone.
Clue 4: The first two digits add to 13. That leaves 1 of the 7, and that is the one.
Down to a handful the last clue chooses between — 8060, 8150, 8240, 8330, 8420, 8510, 8600 — and it keeps just 8510. Seeing the finalists is the point: the answer is picked from them, not guessed, and the clues could have been taken in any order — only the counting changes.

How it works.

01
Nothing is given except statements, and the first thing to fix is how much room there is to search: a four-digit number runs from 1000 to 9999, so there are 9000 of them and 4 clues to get down to one.
02
Do not try to guess a number and check it against the clues — that is 9000 guesses in the worst case. Take the clues one at a time instead, and keep only the numbers still standing after each. The count going down is the working.
03
First clue: The ones digit is even. That leaves 4500 of the 9000, roughly halving it.
04
Clue 2: The thousands digit is 8 more than the ones digit. That leaves 100 of the 4500, which is most of them gone.
05
Clue 3: Its four digits add up to 14. That leaves 7 of the 100, which is most of them gone.
06
Clue 4: The first two digits add to 13. That leaves 1 of the 7, and that is the one.
07
Down to a handful the last clue chooses between — 8060, 8150, 8240, 8330, 8420, 8510, 8600 — and it keeps just 8510. Seeing the finalists is the point: the answer is picked from them, not guessed, and the clues could have been taken in any order — only the counting changes.