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Math Help - Finding the specific digit of a large number

  1. #1
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    Finding the specific digit of a large number

    Hi



    I have absolutely no idea where to start.

    Please help!

    Thanks, BG
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  2. #2
    Senior Member TheAbstractionist's Avatar
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    There are 9 1-digit numbers, 90 2-digit numbers, 900 3-digit numbers and 9000 4-digit numbers. Hence the last digit of the last 4-digit number is in position 9+2\times90+3\times900+4\times9000=38889.

    The last digit of the last 5-digit number will be in position 38889+5\times90000=488889 which is greater than 206787. Hence the number we are looking for is a 5-digit number. The position of the last digit of the 5-digit number N is 5(N-9999)+38889=5N-11106. Now find the largest N such that 5N-11106\le206787.

    5N-11106\,\le\,206787

    \implies\ 5N\,\le\,217893

    \implies\ N\,\le\,43578.6

    So that number is N=43578, whose last digit is in position 206784. The next 5-digit number is 43579 and the 206787th digit in the sequence is the 3rd digit of this number, which is 5.
    Last edited by TheAbstractionist; June 23rd 2009 at 10:09 AM.
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