Posers and Puzzles

Posers and Puzzles

Redundant Digits

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Posers and Puzzles 30 Mar '21 22:49
  1. R
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    30 Mar '21 22:49
    How many integers between 1000 and 9999 inclusive have at least one repeated digit?
  2. Standard memberBigDogg
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    31 Mar '21 02:16
    @joe-shmo said
    How many integers between 1000 and 9999 inclusive have at least one repeated digit?
    Do numbers like 1030 count? [two zeros, but not back-to-back]
  3. R
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    31 Mar '21 02:27
    @bigdoggproblem said
    Do numbers like 1030 count? [two zeros, but not back-to-back]
    Yeah, the 0 is considered a repeated digit in your example.
  4. Standard memberAThousandYoung
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    31 Mar '21 04:302 edits
    @joe-shmo said
    How many integers between 1000 and 9999 inclusive have at least one repeated digit?
    Easiest approach to this is to find how many DON'T have a repeat.

    Reveal Hidden Content
    10x9x8x7=5040

    Reveal Hidden Content
    9999-1000=8999

    Reveal Hidden Content
    8999-5040=***3959***
  5. Standard memberBigDogg
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    31 Mar '21 04:38
    @AThousandYoung

    The method is right, but there are two errors in the arithmetic.

    1)
    Reveal Hidden Content
    There are 9999-1000+1 = 9000 total numbers (do not forget to count the number 1000 also).


    2)
    Reveal Hidden Content
    The thousands digit has only NINE possibilities; it cannot be 0. 9*9*8*7 = 4536


    Solution:
    Reveal Hidden Content
    9000 - 4536 = 4464
  6. R
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    31 Mar '21 11:36
    @BigDoggProblem

    Correct!
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