1. Joined
    21 Jul '06
    Moves
    0
    30 Jul '06 02:573 edits
    Originally posted by perihelion
    And we have a winner!

    For those still trying to figure it out, Bowmann's observation that most of them are composites is on the right track. Keep looking in this direction for something more specific.
    2006 = 2 * 17 * 59

    351 = 3 * 3 * 3 * 13

    378 = 2 * 3 * 3 * 3 * 7

    386 = 2 * 193

    428 = 2 * 2 * 107

    463 is prime

    So what?

    Anyway, if factoring - and then manipulating the factors - of 25 numbers one-by-one is not trial and error, what do you call it? ('Boring' might be a good start.)
  2. Joined
    12 Aug '05
    Moves
    2866
    30 Jul '06 03:50
    Originally posted by ThudanBlunder
    2006 = 2 * 17 * 59

    351 = 3 * 3 * 3 * 13

    378 = 2 * 3 * 3 * 3 * 7

    386 = 2 * 193

    428 = 2 * 2 * 107

    463 is prime

    So what?

    Anyway, if factoring - and then manipulating the factors - of 25 numbers one-by-one is not trial and error, what do you call it? ('Boring' might be a good start.)
    Just a warning, this might give away some key hints, so don't read if you're intent on figuring it out yourself:


    Actually, its the factorization of the other numbers that really matters, and observing that there are some that don't follow the pattern (which end up being part of the set that adds up to 2006).

    I do agree, now that I think about it, that finding a common factor wasn't obvious, and it does take a good bit of patience to figure out what it is. I guess it would have been a lot less frustrating with smaller numbers. But there is a pretty interesting reason why theres a unique solution.
  3. Joined
    11 Jun '06
    Moves
    3516
    30 Jul '06 08:47
    i didn't really use factoring, here's my HINT

    write the #s in increasing order in the following manner
    308 308+a 308+b 308+c etc. where a b c are in increasing order
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