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First of all, it doesn't. The hour-hand and minute-hand align in opposite directions

only 22 times in 24 hours.

The reason is simply because the hands of an ordinary 12-hour analog clock go through

every possible orientation every 12 hours ... twice in 24 hours ... and if you take a clock,

set it to 12:00, and then crank it through 24 hours, you'll see the hands line up in a

180-degree angle 22 times.

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