Solution to Spring 2016 POTW #3 (Stop, Clock, and Roll)

See here for the original post of the puzzle.

Since Clock A is gaining 1 minute every 24 hours, and Clock B is losing 1 minute every 24 hours, then the next time they will all show noon at the same moment will be when Clocks A and B both gain/lose (respectively) 12 hours (meaning they've gotten "closer together" by 24 hours).

Since they lose/gain 1 minute every day, and there are 12 x 60 = 720 minutes in 12 hours, then it will take 720 days to reach that phenomenon.

Thus, we are looking for the date that is 720 days after January 1, 2016. Be careful because 2016 is a Leap Year! So, the final answer is December 21, 2017.

Solution to POTW #1: the broken pocketwatch

See this link for the original puzzle post.

Solution:

We know the watch was correct at 2:00am. Let’s make a table of times, showing both the actual time and the time that the watch shows:

Actual time	Watch time
2:00 am	2:00 AM
3:00 AM	3:36 AM
4:00 AM	5:12 AM
5:00 AM	6:48 AM
6:00 AM	8:24 AM

Voila! When the watch stopped, showing 8:24am, it was actually 6:00am. Since that was one hour ago, it must now be 7:00 am.

“Alternative” method: We can take an algebraic approach instead of making a table of values and hoping to get lucky. Let X denote the number of hours that have passed since 2:00 am, when the watch last showed the correct time. Then, we can set up an equation that represents the time that the watch shows:

The left-hand side says, “The watch shows 8:24am right now”. The right-hand side says, “It was 2, and every hour that passed, the watch gained 1 hour and 36 minutes.”

Solving for X yields X = 4. That is, 4 hours passed since 2:00am, so the actual time was 6:00am when the watch showed 8:24am. Again, since it’s now one hour later, the time must now be 7:00 am.