## Monday, September 28, 2009

### Midday Nap Puzzle

Have you heard the latest news? Grabbing an hour's sleep during the day may be as beneficial for learning as a whole night in bed, according to scientists. So, you decide to boost your learning and memory and start taking a midday nap. You fall asleep at noon and are awaken some time later by your boss standing right next to you. You notice that the minute and hour hands on his watch coincide. How long did you sleep?

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Alin Grin said...

01:11:00

1 Hour and 11 minutes

Maria said...

It looks like it should be right, but I don't think it is. Watch's hands are definitely meeting somewhere between 1pm and 2pm marks. If hour hand is between 1 and 2, then minute hand should be between 5mins and 10mins. But when exactly? Please explain your solution.

Alin Grin said...

Every 10 moves of the minutes hand the hour hand moves 1 time.
after 60 minutes of nap the minutes hand moved 60 times and completed a full cycle and the hour hand moved 10 times (pointing at 10 minutes past the hour and at 1:00 hours). After 10 more minutes the minute hand moved 10 times pointing at 1:00 hours or 10 minutes and the hour hand moved 1 position. Next minute the hour hand does not move and the minute hand moves 1 position and aligns itself with the hour hand. Then the time is 01:11:00. The hand will stay aligned for the whole minute.
So the wake up was between 01:11:01 to 01:11:59.

Barry said...

I think the answer is 1:05. At 1:05, the minute hand has completed 5/60 or 1/12 of the way around the clock, so the hour hand should be 1/12 of its way towards the 2. Assuming the hour hand takes 5 discrete steps to go from the 1 to the 2 on the clock, it should still be pointing directly at the 1 by the time the minute hand is pointing at the 1 at 1:05. I would say the hour hand doesn't take its first step towards the 2 until 1:12.

Maria said...

Alin, it hurts me, because you were the first and because you were so close to the answer. But I think Barry is right and handles will meet around 1:05
One more puzzle for Barry! Go get Alin with his 23 puzzles lead.
Alin, I think you forgot that there only 5 minutes in-between hour marks. Hour hand moves 5 times from 12 to 1, and minute hand moves 5 times from 12 to 1, catching up with the hour hand around 1:05 next to 1 hour mark.

prluhmann said...

How do you know its 1:05? Could it not be 2:10, or 3:15, etc.

Maria said...

Welcome new puzzle solvers!
You are absolutely right - handles will coincide many more times throughout a day. We could only hope that our nap did not last more than 1:05
At least the idea was to take an hour to sleep as scientists recommend.