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Math Help - Please help!

  1. #1
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    Question Please help!

    abcde is a number.When they multiplie 4,they have edcba.
    abcde*4=edcba.Define abcde.
    Thanks!
    Me! sody
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by luckyvan
    abcde is a number.When they multiplie 4,they have edcba.
    abcde*4=edcba.Define abcde.
    Thanks!
    Me! sody
    1. a must be 1 or 2, as if it were any larger abcde*4 would have 6 digits

    2. 4*abcde is even so a must be 2.

    3. if a=2 then e is 8 or 9, as the leading digit on the RHS is either 4*a or 4*a+1.

    4. if a is 2, then consider the trailing digit on the RHS, this a the solution of: 4*x=2 mod 10, which has solutions modulo 10 of 3 and 8, but we know from 3. above that e is either 9 or 8, so it must be 8.

    5. We now know there is no carry from 4*b - otherwise e would be 9 its not so there is no carry. This means that b is either 0, 1 or 2, but 2 is taken so it is either 0 or 1.

    6. Now trial and error can be used, and we find that abcde=21678.

    RonL
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