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when a 3 digits number is reversed, the number decreases by 396. the diffrence between the digits at the units place and the digit at the tens place is the same as the difference between the digits at the tens place and the hundreds place. if the product of 3 digits number is non zero then how many such 3 digits numbers are possible

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Madhurima Mishra

  1. 100u+10t+h = 100h+10t+u - 396
    u-t = t-h

    solve that and you get

    t = h-2
    u = h-4

    h = t+2 = u+4

    since no digit is zero, we can have

    531
    642
    753
    864
    975

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    Steve

  2. let the hundreds, tens , and unit digits be
    x , y, and z respectively .

    so the original number is
    100x + 10y + z

    the number reversed is
    100z + 10y + x

    100x + 10y + z - (100z + 10y + x) = 396
    99x - 99z = 396
    x - z = 4
    x = z+4

    z - y = y - x
    2y = z+x
    y = (z+x)/2

    " if the product of 3 digits number is non zero "
    What does that mean??
    xyz ≠ 0 ???

    cases:
    z = 0, x = 4 , y = 2
    number is 420 , but the product is zero

    z = 1 , x = 5, y = 3
    number is 531

    z = 2 , x = 6, y = 4
    number is 642

    z = 3 , x = 7, y = 5
    number is 753

    z = 4, x = 8 , y = 6
    number is 864

    z = 5, x = 9, y = 7
    number is 975

    z = 6, x = 10, not possible

    so the cases that work are:
    531, 642, 753, 864, and 975

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    Reiny

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