A clock strikes one at 1 o' clock, twice at 2 o'clock and so on, up to twelve times at 12 o'clock. How many times will the bell strike in the course of 2 days?

A standard wall clock operates on a 12-hour dial system, meaning the identical striking pattern repeats twice every single day.
The total number of strikes across one full 12-hour cycle forms a simple arithmetic progression:

$$\text{Strikes in 12 hours}=1+2+3+\cdots +12$$

Using the sum formula for the first $n$ natural numbers, $S=\frac{n(n+1)}{2}$:

$$\text{Strikes in 12 hours}=\frac{12\times 13}{2}=78$$

Since 1 day has 24 hours, it comprises 2 full cycles. Therefore, 2 days contain 4 complete cycles of 12 hours each:

$$\text{Total strikes in 2 days}=78\times 4=312$$