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Seq.(Seq.(Seq.)) seeking sod (Posted on 2009-03-01) Difficulty: 2 of 5
A sequence {S(x)}, each of whose terms is a positive integer, is defined as:

S(x) = x/2, if x is even, and:

S(x) = x+3, if x is odd

Given that n is an odd positive integer and, S(S(S(n))) = 27, determine sod(n).

Note: sod(n) denotes the sum of the base-10 digits of n.

No Solution Yet Submitted by K Sengupta    
Rating: 1.0000 (1 votes)

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Solution Working Backwards | Comment 1 of 3
The inverse of S(x) is 2x, and also x-3 if x is even

If S(S(S(n))) = 27,

(a) then S(S(n)) is 54

(b) then S(n) is 108 or 51 (two possibilities)

(c) then n is 216 or 102 or 105 (three possibilities)

(d) but if n must be odd, then it is 105 and sod(n) = 6

Edited on March 2, 2009, 9:32 am
  Posted by Steve Herman on 2009-03-01 13:27:28

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