Solution #7: The Striking Clock
The strike I heard was either one o'clock or some half hour. If, after another
half hour I hear two more strikes, I know what hour it is, but if I again hear
one strike, I may have heard successively 12:30 am and 1 o'clock or 1 o'clock
and 1:30 am. After another half hour I either hear 1 strike (1:30 am) or two
strikes (2 o'clock). I may, therefore, have to lie awake a whole hour before
I can be sure of the exact time.
Source: Longley-Cook, L. H.