## Wednesday, March 31, 2010

### Clocks in a Line

How many times a day do the hour and minute hands on a clock line up exactly with each other?

1. 24 times? At each hour the minute hand sweeps over the hour hand so they have to line up exactly at each hour.

2. I guess the answer should be 24.

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3. I think the answer is 22. For the hours of 12AM/PM, the minute hand sweeps over the hour hand instantaneously at 12:00. For the hours of 11AM/PM, the minute hand "sweeps" over the hour hand at the very end at 12:00AM/PM. These states seem to be the same and therefore shouldn't be counted twice.

4. 1440 times, Each time the minuit hand goes around it eventually matches up with the hour hand so the awnser is the same as the number of minuits in a day. 24 hours*60minuits/hour = 1440

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