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.

This seemed really simple to me.  I factored the number and got 7, 5, 3^4, 2^7.  Simply pair up four 2s with the 3s to get:

2, 2, 2, 6, 6, 6, 6, 5, 7

That's nine numbers, their product is 9!, and adding them yields 45.

Woo.