# Completing the letter series:

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?

• Ops... I counted one of the spaces in the question too (the one between the two underscores). I'll delete my comment then. – Bojidar Marinov Oct 14 '15 at 10:35
• 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? – Marconius Oct 14 '15 at 14:12
• No. Unfortunately it doesn't give any clue. @Marconius. – Aditya Agarwal Oct 14 '15 at 15:24
• From where did you get the other answer. Are you sure it's not a typo in a book? – ghosts_in_the_code Oct 15 '15 at 15:36
• Okay, I am not sure. Let me update. @ghosts_in_the_code. – Aditya Agarwal Oct 15 '15 at 16:00

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.

• I think that was a misprint. This is the most convincing answer I got so far. – Aditya Agarwal Oct 25 '15 at 5:31

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?