If you think that you are the master of angles then try this


Some of you may have run into those problems where you have to figure out the angle between the two hands of a clock at weird times. Well, I took that problem as a starting point and added a twist to it.

Consider a 12-hour analog clock with two hands and a round face. Consider the angle between the two hands at any given time and, when the angle between the hands is not 180 degrees, take the smaller of the two angles. Thus, at 12:00 the angle between the two hands is 0 degrees. At 3:00 and at 9:00 it’s 90 degrees.

If we me measure the angle between the two hands at each of the 61 consecutive minutes between 12:00 and 1:00 inclusively, what is the sum of those 61 angles?