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Math Help - 4 digit PIN number - please help

  1. #1
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    4 digit PIN number - please help

    I am stuck with this puzzle

    I have forgotten my 4 digit PIN number

    However, I can remember the following facts:

    the first and last digits add up to 10
    the first digit is greater than the last digit
    the four digits add up to 16
    the difference between the last two is 2

    QUESTIONS:

    Make a list of the 7 possible numbers which fit the facts above.


    What is the probability that the 4 digit number had two digits the same?


    What is the probability that it is not the correct PIN Number?
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  2. #2
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    Sorry! Misread the problem.
    Last edited by Soroban; January 28th 2010 at 09:51 AM.
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  3. #3
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    It can't be.

    6154 or 6244 or 6334 or 6514 or 6604 as the difference between the last two digits needs to be 2
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  4. #4
    Senior Member Dinkydoe's Avatar
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    Soroban's final answers are correct, but he misread the question.
    He used that the difference between first and last number was 2.
    We have:

    Spoiler:

    9**1
    8**2
    7**3
    6**4

    As possible pin-numbers combining (1) and (2)

    Combining these with (3), (4): Since the first and last number add up to 10. Because of (3) the second and third number must add up to 6.
    If we combine that with (4) we find possible numbers:

    9331
    8602
    8242
    7513
    7153
    6424
    6064

    Then the probability that 2 digits are the same is: \frac{4}{7}

    The possibility that it's the incorrect number is: \frac{6}{7}

    Just like Soroban said.

    The last question has ofcourse nothing to do with how the numbers look like:



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  5. #5
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    9331, 8242, 7153, 6064, 8602, 7513, 6424
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