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| SOD (Posted on 2008-07-09) |
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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))).
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Submitted by pcbouhid
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Rating: 4.0000 (1 votes)
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Solution:
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(Hide)
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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
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Subject |
Author |
Date |
 | Solution | Dej Mar | 2008-07-09 21:27:18 |
| Solution | K Sengupta | 2008-07-09 11:37:01 |
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