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?

To be precise, you'd need to stay awake just a tiny bit longer than one hour (from the time you hear the single strike).

If it's 12:30 when you hear the single strike and you wait an hour, you are bound to hear another strike no matter what time it is. The key is whether you hear a second strike right after the first (in which case the first single strike you heard was 1:00 and an hour later it is 2:00) or not (in which case the first single strike you heard was at 12:30, and an hour later it is 1:30. So if the chimes ring at a pace of one per second, you'd need to wait an hour and one second from the initial single strike before being certain of whether it was 1:30 or 2:00.

I guess the question is asking how long you had been awake _before_ hearing the single chime. If the question wants the _total_ time, you have to be awake 90 minutes and one second, <s>minus the amount of time it took for the original 12 chimes, i.e. 12 seconds. So 89 minutes and 49 seconds</s> actually, the worst case senerio is then that you woke up at 12:30, in which case the clock only chimed a single time, so you don't need to subtract the 12 seconds..

Edited on August 11, 2005, 7:39 pm

Edited on August 11, 2005, 7:40 pm

Posted by Sam on 2005-08-11 19:31:46