maths can be fun

THE HANDS OF A CLOCK COME TOGETHER

How many positions are there on an ordinary clock with the hour hand and the minute hand in a coincident position?

we can take advantage of the equations derived when solving the proceeding problem; for if the hour hand and the minute hand can be brought to coincidence,  then they can be inter changed, and nothing will change. In this procedure, both hand cover the same number of division from the number 12, or x=y. Thus, from the reasoning of the preceding problem we can derive the equation

 -=m

Where m is an integer between o and 11. From this equation we find

x.

Of the twelve possible values for m (from 0 to 11) we get 11(not 12) distinct positions of the hands because when m=11 we find x=60, that is, both hands cover 60 divisions and arrive at 12; the same occurs when m=0.