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.

Spring 2016 POTW #3: Stop, Clock, and Roll

Submissions due by midnight on Sunday, April 3, 2016.

On this New Year's Day (January 1, 2016), at precisely 12:00 noon, I set up three clocks in my office. Let's call them Clock A, Clock B, and Clock C.

The next day, at precisely noon, I checked on them and discovered that Clock A had gained exactly 1 minute, Clock B had lost exactly 1 minute, and Clock C was right on time.

Assuming that the same rate of gaining/losing time continues on these clocks, When is the next date on which all three clocks will show precisely noon at the same moment? (That is, your answer should be a specific date, like "May 6, 2025" or something.)

(Use the submission box below to submit your answer. No need to explain: a correct answer will suffice for 10 points. However, feel free to explain your answer if you want a chance at some partial credit, in the event that your answer is incorrect.)