Why Do Clock Hands Sometimes Overlap Exactly 11 Times?

The Fast and Slow Dancers

Imagine a minute hand running in circles around a clock face. It is super fast. Now look at the hour hand. It moves slowly like a sleepy turtle. Every hour, the minute hand tries to catch up to the hour hand. You might think they shake hands twelve times because there are twelve numbers on the clock.

The Missed Spot

But wait! When the minute hand catches the hour hand exactly at 12:00, they start together. As time goes by, the hour hand keeps creeping forward a little bit each time the minute hand laps it. Because the hour hand is moving away, the minute hand has to run just a tiny bit further to catch it.

By the time you get to the end of twelve hours, that extra creep adds up. The hands do not quite meet again at the very last second mark before starting over. So instead of meeting twelve times, they only meet eleven times in half a day! It is like two friends walking; if one keeps stepping forward while the other waits, they will cross paths slightly less often than you would expect.