When the digits of a positive integer are written in reverse to form a new positive integer with the same number of digits(e.g., 1234 4321), the new number is 90 less than the original. What is the smallest possible value of the original number?

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asked by PT
  1. Case 1: a 2 digit number
    in the original, let the unit digit be y and the tens digit be x
    so the number is 10x + y and the reverse digit number is 10y + x
    we have 10y + x - 10x - y = 90
    9y - 9x = 90
    y - x = 10 , no such numbers since both x and y must be less than or equal to 9
    Case 2: a 3 digit number
    arguing as above
    100x + 10y + z - 100z - 10y - x = 90
    99x - 99z = 90
    11x - 11z = 10
    11(x-y) = 10 none

    case 3: 4 digit numbers
    how about 1211 and 1121 , did not say we can't repeat digits.

    1211 - 1121 = 90

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    posted by Reiny

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