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Lê Quốc Trần Anh Coordinator

26/07/2018 at 01:38
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A two-digit number formed by any 2 adjacent digits of a 2017-digit number is divisible by 17 or 23. If the last digit of the 2017-digit number is 1, find the first digit.


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    Tôn Thất Khắc Trịnh 27/07/2018 at 04:37

    Starting with 1, the first number formed is definitely going to be 51 being divisible by 17.
    Then it's 85 divisible by 17.
    Then it's 68 divisible by 17.
    Now it's 46 divisible by 23.
    And it's 34 divisible by 17.
    And it's 23 divisible by 23.
    And now it's 92 divisible by 23.
    Here, it's 69 divisible by 23
    And it's 46 divisible by 23
    And it repeats...
    SO the patter is always ...(92346)851 (The things in the parenthesis are repeating)
    Since it's 2017 digits, the loop would end on the (2017-3) mod 5 = 4th number being 2
    THE FIRST DIGIT IS 2

    Lê Quốc Trần Anh selected this answer.

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