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Math Help - Ever notice this?

  1. #1
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    Ever notice this?

    Select a four-digit number (other than a multiple of 1111).

    (1) Arrange the digits in decreasing order.
    (2) Arrange the digits in increasing order.
    (3) Subtract these two numbers.
    (4) Repeat steps (1), (2), (3) with this new number.

    Repeat step (4) until you are sleepy.


    Exanple: . 1728

    8721 - 1278 \:=\:7443

    7443 - 3447 \:=\:3996

    9963 - 3699 \:=\:6264

    6642 - 2466 \:=\:4176

    7641 - 1467 \:=\:6174

    7641 - 1467 \:=\:6174

    . . . \vdots . . . . . . . \vdots

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  2. #2
    Member Glaysher's Avatar
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    Quote Originally Posted by Soroban View Post
    Select a four-digit number (other than a multiple of 1111).

    (1) Arrange the digits in decreasing order.
    (2) Arrange the digits in increasing order.
    (3) Subtract these two numbers.
    (4) Repeat steps (1), (2), (3) with this new number.

    Repeat step (4) until you are sleepy.


    Exanple: . 1728

    8721 - 1278 \:=\:7443

    7443 - 3447 \:=\:3996

    9963 - 3699 \:=\:6264

    6642 - 2466 \:=\:4176

    7641 - 1467 \:=\:6174

    7641 - 1467 \:=\:6174

    . . . \vdots . . . . . . . \vdots

    Yes, you get Kaprekar numbers
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  3. #3
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    What happens with 5 digits, 6 digits, etcetera? Are there any 4 digit nbrs that don't wind up at 6174, apart from 1111 etc?
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  4. #4
    Member Glaysher's Avatar
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    Quote Originally Posted by ray_sitf View Post
    What happens with 5 digits, 6 digits, etcetera? Are there any 4 digit nbrs that don't wind up at 6174, apart from 1111 etc?
    Kaprekar Number
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