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Math Help - How many 10 digit positive integers with at most 7 consecutive zeros?

  1. #1
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    How many 10 digit positive integers with at most 7 consecutive zeros?

    How many 10-digit positive integers with no leading zeros (i.e., integers from 1,000,000,000 to 9,999,999,999) have at most 7 consecutive zeros? For example, the number 3,000,000,200 has 8 zeros but they are not all consecutive and therefore this number should be counted. On the other hand, the number 8,000,000,001 has 8 consecutive zeros and should not be counted.
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  2. #2
    Senior Member abhishekkgp's Avatar
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    first find out the number of numbers with exactly 7 consecutive zeros, 8 consecutive zeros and 9 consecutive zeros. sum all these up and subtract from the total number of 10 digit numbers.
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  3. #3
    Senior Member abhishekkgp's Avatar
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    in my last post i committed a mistake. you dont have to subtract the number of numbers having exactly 7 consecutive zeros since the question allows the counting of these numbers.

    so to get the answer find:
    (total number of 10 digit numbers) - [(number of numbers having exactly 8 consecutive zeroes)+(number of numbers having exactly 9 consecutive zeros)]
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