Number theory · Divisibility · Coprimality · Linear congruences · Clock angles
A clock has three hands, each turning at its own constant speed: the second hand completes a full circle in one minute, the minute hand in one hour, and the hour hand in twelve hours. At midnight all three hands are in the same position. How many times during the following \(24\) hours will one of the hands make an angle of \(30^\circ\) with each of the other two?
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Serbian Municipal Competition 2018, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source