Discussion
A clock strikes once at 1 O'clock, twice at 2 O'clock, thrice at 3 O'clock and so on. How many times in total will it strike in 24 hours ?
Answer: A
The clock strikes 156 times in 24 hours.
In each 12-hour cycle it strikes 1 + 2 + ... + 12 times, and a day has two such cycles.
\[ \begin{aligned} 1 + 2 + \cdots + 12 &= \frac{12 \times 13}{2} = 78 \\ 2 \times 78 &= 156 \end{aligned} \]
144 is \(12 \times 12\), which treats every hour as 12 strokes, and 164 and 168 match no counting rule. The key step is remembering that the 1-to-12 cycle happens twice a day.
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