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?

Actually, it passes 11 times in every 12 hour period as Ender specitied in his initial comment. As a result, it will only pass 22 time in each 24 hour period. (Quite simple actually if you think that the hour hand has gone around two times.) The 23rd time will be at 12am (assuming that you started counting at midnight) the following morning. So 22 times in 24 hours.

Posted by Popstar Dave on 2003-09-08 09:42:35