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.

(In reply to

Answer by K Sengupta)

At the outset, we know that (1,2,3,4,5,6,7,8,9) is a trivially valid solution..

Now, we observe that 3+6+8 = 4+4+9 and 3*6*8 = 4*4*9

Hence, removing the numbers 3, 6 and 8 from the above set and adding respectively 4, 4 and 9 in its place we obtain the required 9 integers having the desired property as 1, 2, 4, 4, 4, 5, 7, 9, 9

*Edited on ***December 12, 2012, 12:05 pm**