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Who am I? number puzzles

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The question

I am a four-digit number. The ones digit is even. The thousands digit is 8 more than the ones digit. Its four digits add up to 14. The first two digits add to 13.

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
  1. A four-digit number runs from 1000 to 9999 — 9000 of them — and 4 clues narrow it down to one.
  2. Take the clues one at a time, and keep only the numbers that still fit after each.
  3. First clue: The ones digit is even. That leaves 4500 of the 9000, roughly halving it.
  4. Clue 2: The thousands digit is 8 more than the ones digit. That leaves 100 of the 4500, which is most of them gone.
  5. Clue 3: Its four digits add up to 14. That leaves 7 of the 100, which is most of them gone.
  6. Clue 4: The first two digits add to 13. That leaves 1 of the 7, and that is the one.
  7. Before the last clue, 7 were left — 8060, 8150, 8240, 8330, 8420, 8510, 8600 — and it keeps just 8510.

How it works.

  1. 01

    A four-digit number runs from 1000 to 9999 — 9000 of them — and 4 clues narrow it down to one.

  2. 02

    Take the clues one at a time, and keep only the numbers that still fit after each.

  3. 03

    First clue: The ones digit is even. That leaves 4500 of the 9000, roughly halving it.

  4. 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.

  5. 05

    Clue 3: Its four digits add up to 14. That leaves 7 of the 100, which is most of them gone.

  6. 06

    Clue 4: The first two digits add to 13. That leaves 1 of the 7, and that is the one.

  7. 07

    Before the last clue, 7 were left — 8060, 8150, 8240, 8330, 8420, 8510, 8600 — and it keeps just 8510.

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