Problem

Source: Spring 2005 Tournament of Towns Junior A-Level #3

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Baron Münchhausen’s watch works properly, but has no markings on its face. The hour, minute and second hands have distinct lengths, and they move uniformly. The Baron claims that since none of the mutual positions of the hands is repeats twice in the period between 8:00 and 19:59, he can use his watch to tell the time during the day. Is his assertion true? (5 points)