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4 digit number knowing one number

  1. Feb 28, 2012 #1
    I can't get started on this. If I am trying to figure out a 4-digit number, and I know one of the numbers, but not which digit it is, how many possible numbers are there?
  2. jcsd
  3. Feb 28, 2012 #2

    Simon Bridge

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    Welcome to PF.
    The trick is to think of it like this: you have four slots which can take a single digit each - the four digits make one number.

    There are four possible places that the known digit can be in.
    So the answer must be four times the number of ways that the remaining three digits can be arranged.
    There are 10 possible digits.

    Presumably you have just been doing permutations and combinations?
  4. Feb 29, 2012 #3
    I have questions.

    Is this digit you know different from all of the other digits?

    You are not allowing 0 for a first digit?
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