... Here's the problem:
Visualize an analog 12-hour clock with hour hand, minute hand, second hand. We know that at 12:00:00 all three hands are in perfect mathematically defined alignment. At what other times if any (such as five minutes and a few seconds after one, or maybe 21 or 22 minutes and a few seconds after four) are all three hands in perfect alignment. Prove (or disprove) it...
Prove what exactly?
Off the top of my head, the clock hands would align eleven times as the hour hand travels around the clock face. The minute hand must run around 60 minutes plus five minutes (1/12th of the next hour) to catch up with the hour hand.
The second hand only matters when the other two are aligned, as it next catches up with the minute hand every 1+1/12th hour.
It is way past bedtime here, so if I messed this up, that is my excuse...
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