How many times to the hands of a clock form a 60 degree angle between noon and midnight on the same day?
Firstly im not sure weather they require the second hand to be included.
And secondly (excuse the pun) i have no clue how to start the problem.
Thanks.
Best Answer
Hint
Total angle swept by the pins on a clock $ = 360^{\ \text{o}} $
Smallest unit on clock (for recreational questions, second hand is NOT taken into consideration) $ = 1 $ minute
$ \therefore $ Area swept per minute $ \implies 6^{\text{ o}} $.
Hence, to generate an angle of $ 60^{\text{ o}} $ (between hour and minute hands), they should be $ 10 $ units apart.