Home > Just Math
| SOD (Posted on 2008-07-09) |
 |
Denote "sod(x)" as sum of the digits of x. Examples: sod(49) = 4 + 9 = 13; sod(123) = 1 + 2 + 3 = 6.
Find sod(sod(sod(4444^4444))).
|
|
Submitted by pcbouhid
|
|
Rating: 4.0000 (1 votes)
|
|
|
Solution:
|
(Hide)
|
Besides KS and Dej Marīs solutions, another way:
let X = 4444^4444
4444^4444 has 4444*log(4444) + 1 = 16,211 digits
So, sod(X) <= 9 * (# of digits) < = 9*16,211 <= 145,900
sod(sod(X)) <= sod(99,999) = 45
sod(sod(sod(X))) <= sod(39) = 12
but sod(sod(sod(X))) (congr) 7 (mod 9), because 4444^4444 (mod 9) (congr) 16^16 (mod 9) (congr) 7^7 (mod 9) (congr) 823543 (mod 9) (congr) 7 (mod 9)
thus sod(sod(sod(X))) = 7
|
Comments: (
You must be logged in to post comments.)
| |
Subject |
Author |
Date |
 | Solution | Dej Mar | 2008-07-09 21:27:18 |
| Solution | K Sengupta | 2008-07-09 11:37:01 |
|
|
Please log in:
Forums (0)
Newest Problems
Random Problem
FAQ |
About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On
Chatterbox:
|
