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. S24 = 24+1+2+3+...20+21+22+23 We may as well move the 24 from the left end to the right end. S24 = 1+2+3...20+21+22+23+24 Sn =(a1 + an) n = 24, a1 = 1, an = a24 = 24. S24 = (1 + 24) S24 = 12×25 = 300 times. Edwin