Clocks Here's how I prefer to explain the fact that the hour and the minute hand pass 11 times in 12 hours: You have 12 clocks. None of them are running. They are all set to 12:00. At noon, you start the first one ticking. It ticks ad ticks and some time shortly after 1 AM, the minute hand passes the hour hand. At the very moment that occurs, you let the second clock run from its 12:00 position. Now, the hour and the minute hands on the two clocks are spinning at the same rates, so clearly the angle between them is always the same on the first clock as it is on the second. Some time later, the second clock passes 1:00 and its hands overlap. At this same time, the first clock's hands must overlap too (angle is zero). At that precise moment, you set the 3rd clock in motion. Etc etc etc. Every time the hands overlap on the first clock, they also overlap on every other clock, and they are all running staggered by the same amount of time. By the time midnight rolls around, you have 11 clocks running, and at exactly midnight the hands overlap again on the first clock, at which point you let the 12th clock run. The 12 clocks span 12 hours, and they show you the 11 repetitions of clock hand movement. Clearly, therefore, the interval between repetitions is 12/11 hours. By the way, 00:00:00 are the only times all three hands overlap, and at no times do the three hands evenly divide the circle. meeroh Tuesday, June 03, 2003 simply put it takes 65 minutes for the hands to overlap thus only overlapping 11 times in 12 hours Binyomin Wednesday, June 04, 2003 >it takes 65 minutes for the hands to overlap thus only overlapping 11 times in 12 hours Except that 65 mins * 11 < 12 hours. Brian Tuesday, June 10, 2003 for every x minute the minute hand travels, the hour hand travels x/12 minutes. we start at 12PM.The minute hand takes 60 minutes to reach back at 12. By that time the hour hand has moved 60/12=5 minutes. now by the time the  minute hand reaches there the hour hand has further moved (1/12)*(60/12) minutes... so it finally boils down into a series,   60 +60/12+60/12*12 +... (which is an infinite Geometric Progression)   and the result is     60{1/1-(1/12)}=60*12/11 minutes=12/11 hours. mallu Thursday, June 12, 2003 12 hours huh! are you sure that's the answer if we start at any time! i mean could the answer be 10 times if we start at a specific time? ameer Sunday, July 06, 2003   Fog Creek Home