# 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. Oct 14, 2015 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? Oct 14, 2015 at 14:12
• No. Unfortunately it doesn't give any clue. @Marconius. Oct 14, 2015 at 15:24
• From where did you get the other answer. Are you sure it's not a typo in a book? Oct 15, 2015 at 15:36
• Okay, I am not sure. Let me update. @ghosts_in_the_code. Oct 15, 2015 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. Oct 25, 2015 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?