Question 689037
<pre>
I'll assume that the day starts at the beginning of the 1st
stroke of 24 at midnight, and is over just before it starts 
to strike 24 the second time.  So I will only count the strike
of 24 just once, and not count the striking of 24 at the end. 

S<sub>24</sub> = 24+1+2+3+...20+21+22+23

We may as well move the 24 from the left end to the right end. 

S<sub>24</sub> = 1+2+3...20+21+22+23+24

S<sub>n</sub> = {{{n/2}}}(a<sub>1</sub> + a<sub>n</sub>) 

n = 24, a<sub>1</sub> = 1, a<sub>n</sub> = a<sub>24</sub> = 24. 

S<sub>24</sub> = {{{24/2}}}(1 + 24)

S<sub>24</sub> = 12×25 = 300 times.

Edwin</pre>