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Omni-MATH / It is midnight on April 29th, and Abigail is listening to a song by her favorite…

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problem

It is midnight on April 29th, and Abigail is listening to a song by her favorite artist while staring at her clock, which has an hour, minute, and second hand. These hands move continuously. Between two consecutive midnights, compute the number of times the hour, minute, and second hands form two equal angles and no two hands overlap.

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