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I have been provided the following short puzzle and need help understanding the answer.

Complete the following letter series:
a_abc_ab_ _c_bb_cc_

I filled it like this: aaabcaabbbcabbccca
I had noticed there could be a pattern constructed using blocks of 7 sequential letters (XXXYZXX):

aaabcaa
bbbcabb
ccca...

However, I have been told that the correct answer is aaabcaabbbccbbccca, which differs from my answer in only one place. Please note, I am not sure about the answer. It was taken only as a reference. So please let this undermine your approach.

Can anyone help me understand what makes this answer is correct?

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  • $\begingroup$ Ops... I counted one of the spaces in the question too (the one between the two underscores). I'll delete my comment then. $\endgroup$ – Bojidar Marinov Oct 14 '15 at 10:35
  • $\begingroup$ Is there another clue in the original question that could explain why the official solution has exactly one run of length one, two and three for each of the three letters? $\endgroup$ – Marconius Oct 14 '15 at 14:12
  • $\begingroup$ No. Unfortunately it doesn't give any clue. @Marconius. $\endgroup$ – Aditya Agarwal Oct 14 '15 at 15:24
  • $\begingroup$ From where did you get the other answer. Are you sure it's not a typo in a book? $\endgroup$ – ghosts_in_the_code Oct 15 '15 at 15:36
  • $\begingroup$ Okay, I am not sure. Let me update. @ghosts_in_the_code. $\endgroup$ – Aditya Agarwal Oct 15 '15 at 16:00
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Another sequence that would make sense would be

aaa,b,c,aa,bb,cc,a,bbb,ccc,...

since

the a's decrease and the b's and c's increase in numbers.

That doesn't explain the stated correct answer, though.

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  • $\begingroup$ I think that was a misprint. This is the most convincing answer I got so far. $\endgroup$ – Aditya Agarwal Oct 25 '15 at 5:31
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The only thing I can think is that with the "correct" answer you get a single, double and triple sequence of all 3 letters.

  • triple a,
  • single b,
  • single c,
  • double a,
  • triple b,
  • double c,
  • double b,
  • triple c,
  • single a

I can't find a pattern to that though.

a,b,c,a,b,c,b,c,a

or

3,1,1,2,3,2,2,3,1

Maybe someone else sees it?

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