How Many Times a Day Do a Clock’s Hands Overlap?

How many times a day do a clock’s hands overlap?  I’m going to walk you through the way to solve the problem and then give you an answer.

The way it works is (this is a math formula), in T hours, the minute hand completes T laps.  In the same amount of time, the hour hand completes T over 12 laps.  The 1st time the minute in our hands overlaps, the minute hand is completed one more lap than the hour hand.T=T/12 + 1.  That means the 1st time it overlap occurs after T/11 hours or [1:05] AM.

It, therefore, follows that the 2nd time they overlap the minute hand-completed 2 more laps than the hour hand. we can then conclude that T = T/12  + n.

Since we have 24 hours in a day, the equation can be solved for n.

24 = 24/12+n 24 = 2 + n n = 22

The hands of the clock overlap 22 times a day.

The mass translates at the overlap at:

12, [1:05], [2:11], [3:16], [4:22], [5:27], [6:33], [7:38], [8:44], [9:49], and [10:55] and midnight.

Remember that they repeat themselves for the next sequence.

Ⓒ The Big Game Hunter, Inc., Asheville, NC 2020



Jeff Altman, The Big Game HunterJeff Altman, The Big Game Hunter is a coach who worked as a recruiter for what seems like one hundred years. His work involves career coaching, all as well as executive job search coaching, job coaching, and interview coaching. He is the host of “No BS Job Search Advice Radio,” the #1 podcast in iTunes for job search with more than 1800 episodes, and is a member of The Forbes Coaches Council.

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Jeff Altman, The Big Game Hunter
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