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SOD (Posted on 2008-07-09) Difficulty: 3 of 5
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))).

See The Solution Submitted by pcbouhid    
Rating: 4.0000 (1 votes)

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Solution Solution Comment 2 of 2 |
As 44444444 can be rewritten as (7 + 9*493)(4 + 6*740), the two values 7 (as b, the root base) and 4 (as p, the root power) can be cross-referenced with the following cyclic-power digital root function table, following, to show that the application of the digital root function, S[44444444], yields 7.

b  p=2 p=3 p=4 p=5 p=6 p=7
1:  1   1   1   1   1   1
2:  4   8   7   5   1   2
3:  9   9   9   9   9   9
4:  7   1   4   7   1   4
5:  7   8   4   2   1   5
6:  9   9   9   9   9   9
7:  4   1   7   4   1   7
8:  1   8   1   8   1   8
9:  9   9   9   9   9   9

In this case, sod(44444444) = 72601.  Thus, sod(sod(44444444)) = 7+2+6+0+1 = 16, and, sod(sod(sod(44444444)))  = 1+6 = 7, which equals and confirms the result of S[44444444].

Edited on July 9, 2008, 9:37 pm
  Posted by Dej Mar on 2008-07-09 21:27:18

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