Find nine single digit numbers (other than 1, 2, 3, ..., and 9) with a sum of 45 and a product of 9! (362,880).

For instance, 2, 2, 3, 4, 5, 6, 7, 8, 8 add up to 45, but their product is 645,120.

Try finding the answer without the use of a program.

I found one possible answer being

1,2,4,4,4,5,7,9,9

I broke down each number 1 through 9 to its lowest common multiple, thus giving me: 1,2,3,2x2,5,2x3,7,2x2x2,3x3.  All together being 2x2x2x2x2x2x2x3x3x3x3x5x7.  This way I know that the product will remain correct.

Trial and error got me to the above solution after about 5 different variations.

I just went back and read Charlie's post and he had attacked it the same way as I did.