When Do the Three Hands of an Analog Clock Overlap?

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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?


Contributed by: Frederick Wu (October 2008)
Open content licensed under CC BY-NC-SA



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.

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