3 edits
Originally posted by perihelion2006 = 2 * 17 * 59
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.
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.)
Originally posted by ThudanBlunderJust a warning, this might give away some key hints, so don't read if you're intent on figuring it out yourself:
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.)
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.