When Do the Three Hands of an Analog Clock Overlap?

There is an interesting puzzle based on old-fashioned analog clocks.
Question: How many times a day are the three hands of a clock exactly in line? What are the exact times? How can you calculate them?


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Answer: This Demonstration solves this puzzle by finding the 12 times.
Snapshot 1: the first moment that the three hands overlap is at 0:0:0 or 12:00:00
Snapshot 2: the second moment is at 1:05:05
Snapshot 3: the last moment is at 11:59:59
Tip: The "static" option is for turning the three hands to any position you want.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.