I woke up one night and heard my clock strike "one." I was too tired to turn on the light to see what time it
was. As I lay there pondering, it occurred to me to speculate how long I would have to lie awake in order to be
sure what was the exact time. My clock strikes the hours and strikes "one" each half hour. I fell asleep before I
solved the problem, but can you work out what is the longest time I would have to lie awake after hearing the
strike "one," to be sure of the time?
+130466
One hour...... To see why......Let's suppose that you either awoke at 12:30AM or at 1AM......At each of these times you would have heard a "one."
If you awoke at 12:30AM.....the next "one" you would hear would be at 1AM......But you couldn't be sure if this "one" was to signal 1AM or 1:30AM......But, upon hearing the third "one"- 30 minutes later - you would know that this sequence could only happen at 12:30 AM, 1AM and at 1:30AM
Similarly...if you awoke at 1AM......the next "one" you would hear would occur 30 minutes later - at 1:30AM. But, as before.......you couldn't be sure if this "one" was to signal 1AM or 1:30AM.......so you would have to wait until 2AM - when the clock struck "two" - to ensure the correct time.
In either case, you would have to stay awake one whole hour.......
+130466
One hour...... To see why......Let's suppose that you either awoke at 12:30AM or at 1AM......At each of these times you would have heard a "one."
If you awoke at 12:30AM.....the next "one" you would hear would be at 1AM......But you couldn't be sure if this "one" was to signal 1AM or 1:30AM......But, upon hearing the third "one"- 30 minutes later - you would know that this sequence could only happen at 12:30 AM, 1AM and at 1:30AM
Similarly...if you awoke at 1AM......the next "one" you would hear would occur 30 minutes later - at 1:30AM. But, as before.......you couldn't be sure if this "one" was to signal 1AM or 1:30AM.......so you would have to wait until 2AM - when the clock struck "two" - to ensure the correct time.
In either case, you would have to stay awake one whole hour.......
