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.
To solve this problem, I listed 1 through 9 next to their factors.
1 1
2 2
3 3
4 22
5 5
6 23
7 7
8 222
9 33
I
thought, "Maybe I can arrange the factors differently with the same
sum, 45." So I tried it, first moving the 3 factor of 6 alongside
the 3 factor of 3, changing 3 and 6 to 9 and 2. This increased
the sum to 47. The very next thing I tried was moving one of the
2 factors on the 8 to the 2, changing the 2 and 8 to 4 and 4. I
recalculated the sum and got... 45. I must have made some lucky
guesses.
The factors relisted:
1 1
4 22
9 33
4 22
5 5
2 2
7 7
4 22
9 33
Edit: I sneaked a peek at Charlie's solution... Is this solution unique? Those were some lucky guesses then!
Edited on February 28, 2005, 11:54 pm
|
|
Posted by Tristan
on 2005-02-28 23:52:03 |
Solution
