I have a clock at home that chimes on every hour and half hour mark. On whole hour marks it chimes once for each hour, and on half hour marks it chimes only once.

One night I was wakened suddenly and realized the the clock had chimed, but I did not know how many times. As I lay awake thinking about nothing in particular I heard the clock chime once and started wondering what time it was.

What is the longest amount of time I would have to lie awake before I knew for sure what time it was?

1 hour. If the clock chimed once it could half past sometime or 1 o clock.

If it was half past sometime, then waiting half an hour would tell the time, except if it were halfway past twelve.

If it were half past twelve, half an hour later the clock would chime once again, you would not know if it was 1 o clock or half past one. Wait another half hour, if the clock chimes once again, it is half past one, if it chimes twice it two o clock.

Posted by Avinash Narain on 2005-08-10 07:31:26