Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Two successive digits and divisibility puzzle

  1. Apr 16, 2010 #1
    Determine all possible value(s) of a 8-digit base 10 positive integer having the form ABCDEFGH, where each of the capital letters denotes a different digit from 1 to 9, that satisfy each of the following conditions:

    (I) AB is divisible by 2, and:

    (II) BC is divisible by 6, and:

    (III) CD is divisible by 7, and:

    (IV) DE is divisible by 5, and:

    (V) EF is divisible by 8, and:

    (VI) FG is divisible by 9, and:

    (VII) GH is divisible by 4
     
    Last edited: Apr 16, 2010
  2. jcsd
  3. May 13, 2010 #2
    B C F H @ [2 4 6 8]
    A D G @ [1 3 7 9]

    DE/5 -> E=5
    EF/8 -> EF=56-> F=6
    FG/9 -> FG=63-> G=3
    GH/4 -> GH=32-> H=2

    A D @ [1 7 9]
    B C @ [4 8]

    CD/7 -> CD=49-> C=4, D=9, B=8
    AB/2 -> A=1,7

    ABCDEFGH=18495632, 78495632
    :smile:
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook