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I have frequently seen problems like how many times between _ and _ will the minute and hour hand be together, or be 90 degrees apart.

So if someone can give me a complete solution to the following three parts I would be grateful!

a) How would we find the number of times the minute and hour hand are together from 12:00 a.m and 12:00 p.m?

b) How many times will the minute and hour hand be diametrically opposite?

c) How many times will the minute and hour hand be 90 degrees apart?

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    This might be helpful: [clock related challenge](http://math.stackexchange.com/a/145585/25554).2012-09-15

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