Anne and Mike have an argument about the hands of the clock:

**Anne**: "*The minute hand takes one hour to make a complete circle. Therefore, it will pass the hour hand once every hour!*"

**Mike**: "*But by the time the minute hand has made a full circle, the hour hand will have moved 1/12th of the circle ahead. And by the time the minute hand gets to that spot, the hour hand will have moved forward yet again. This will continue indefinitely, so it is obvious that contrary to what it may seem like, the minute hand will ***never** pass the hour hand."

In reality, how often **does** the minute hand pass the hour hand?

(In reply to

Answer by K Sengupta)

If for some mechanical anomaly, the hour hand remains static throughout but the minute hand can move in its normal speed, then we observe that the minute hand and the hour hand will meet precisely 12 times in 12 hours. ......(I)

However,we know that the minute hand moves 12 times faster than the hour hand in the normal course, so that the minute hand gains 11/12 of the total distance it traverses over the

hour hand.

Consequently, in terms of (I), it follows that the two hands will meet precisely (11/12)*12 = 11 times in every 12 hours.