math

i am a three digit number. my hundreds digit is three more than my ones digit.my tens digit is oneless than my hundreds digit. what numbers can i be?

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  1. d = your digit

    d = 100 x + 10 y + z

    my hundreds digit is three more than my ones

    x = z + 3

    that is equivalent with :

    z = x - 3

    my tens digit is oneless than my hundreds

    y = x - 1

    d = 100 x + 10 y + z

    d = 100 * x + 10 * ( x - 1 ) + x - 3

    d = 100 x + 10 x - 10 + x - 3 = 111 x - 13

    Solution 1 :

    x = 9

    y = x - 1 = 9 - 1 = 8

    z = x - 3 = 9 - 3 = 6

    d = 986

    Solution 2 :

    x = 8

    y = x - 1 = 8 - 1 = 7

    z = x - 3 = 8 - 3 = 5

    d = 875

    Solution 3 :

    x = 7

    y = x - 1 = 7 - 1 = 6

    z = x - 3 = 7 - 3 = 4

    d = 764

    Solution 4 :

    x = 6

    y = x - 1 = 6 - 1 = 5

    z = x - 3 = 6 - 3 = 3

    d = 653

    Solution 5 :

    x = 5

    y = x - 1 = 5 - 1 = 4

    z = x - 3 = 5 - 3 = 2

    d = 542

    Solution 6 :

    x = 4

    y = x - 1 = 4 - 1 = 3

    z = x - 3 = 4 - 3 = 1

    d = 431

    Solution 7 :

    x = 3

    y = x - 1 = 3 - 1 = 2

    z = x - 3 = 3 - 3 = 0

    d = 320

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  2. Just start by putting 0, 1,2, ... into the ones digit
    then fulfilling the other two conditions
    320
    431
    542
    653
    764
    875
    986 , can't use 7 or higher for the unit digits

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