singapore math

My 3rd grade son get this math problem.
It states that John thinks of a 3-digit number. What is his number? Use the clues below to find John's number.

Every digit is different.
The sum of all thedigits is 19.
The difference between the hundreds digit and the ones digit is 6.
The tens digit is the greatest digit.
The number is greater than 500.

Please Help.

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  1. Use trial and error.

    The hundreds digit is 6, 7, 8, or 9

    The ones digit is 0, 1, 2, or 3

    The tens digit is 7, 8, or 9

    Can you figure this out now?

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    Ms. Sue
  2. if hundreds-ones=6, then we have


    Since the digits add to 19, 7x1 and 6x0 are out, leaving

    9x3 or 8x2

    If tens is greatest, 9x3 is out, so we must have


    This must be the number, since the only other choice would be 298, where the difference between hundreds and ones is still 6, but in the other direction

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  3. x y z
    x + y + z = 19
    |x-z| = 6
    x >/= 5
    y >/= 6
    so x+y >/= 11
    so z </= 8 to get 19 sum

    z < 6 because y is biggest
    x 5 6 7 8 9
    y 6 7 8 9
    z 0 1 2 3 4 5 6 7 8
    but x and z differ by 6 so
    x 5 6 7 8 9
    y 6 7 8 9
    z 0 1 2 3
    now what adds to 19 there with y biggest?
    none until y = 9
    so x 9 z
    but x and z differ by six
    8 and 2 differ by six
    8 9 2 ?

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