GeekDad Puzzle of the Week – Time for Reflection

As I sat in a conference room on Friday, I happened to catch the time of clock reflected in the tabletop surface. To my surprise, it made another valid time!

This got me to thinking about how often this occurs, the time difference between occurrences, and the time difference between the source and reflected time. And of course, you guessed it, I am mentioning this as it is this week’s GeekDad Puzzle of the Week!

For your chance at this week’s fabulous prize, please answer the following questions:

• What fraction (or percentage) of the time does the reflected time reflect a valid time?
• What fraction (or percentage) of these times are something different than the current time?
• What is the longest wait between reflected times being valid?
• What is the shortest wait between reflected times being valid?
• What is the largest time difference between the actual time and its reflected time?
• What is the shortest non-zero time difference between the actual time and its reflected time?
• Does using a 24-hour instead of a 12-hour clock (ignoring AM/PM) make any difference to the above questions?

As always, please submit your answers to GeekDad Central. All correct, or at least reasonably well-reasoned responses will be entered into a random drawing for this week’s fabulous prize, a $50 Gift Certificate from ThinkGeek.

Good luck, and happy puzzling!