Discussion
In the series AABABCABCDABCDEABCDEF..., which letter appears at the 261st place?
Answer: C
The 261st letter is H.
The series is built in blocks: A, AB, ABC, ABCD, and so on, block n having n letters. After n blocks the length is \(n(n+1)/2\).
\[ \begin{aligned} \frac{22 \times 23}{2} &= 253 \\ 261 - 253 &= 8 \end{aligned} \]
The first 22 blocks fill 253 places, so place 261 is the 8th letter of block 23, which is H. G is an off-by-one from counting 7 places, and D and L come from miscounting the completed blocks.
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