FILE No.34Unsolved
A jewel was stolen from the great hall of a mansion. As the thief carried it off, he bumped the old wall clock and it stopped.
The stopped clock had its hour hand (short) and minute hand (long) exactly overlapping. The hands point to the 2 a.m. hour. There is no second hand.
The four suspects’ alibis are as follows.
Who has no alibi at the time in the 2 a.m. hour when the hands overlap?
If you get stuck, open the hints one at a time, in order.
How many times in 12 hours do the hour and minute hands overlap?
At about what time in the 2 o’clock hour do they overlap?
Who has no alibi at that time?
Who has no alibi at the time in the 2 a.m. hour when the hands overlap?
Choose the answer closest to the truth.
Aoyagi
The answer is Aoyagi.
In 12 hours the hour and minute hands overlap 11 times, at intervals of 12 / 11 hours. The second overlap is at 2 x (12/11) hours, about 2:10:54 (this is the only overlap in the 2 a.m. hour).
At 2:10:54, Ishiguro (2:08 to 3:00), Usami (until 2:12) and Eguchi (2:00 to 2:30) all have alibis. Only Aoyagi finished his patrol at 2:10, so he has no alibi at 2:10:54.
If you think roughly that "the hands overlap at about 2:10," the alibis lasting until exactly 2:10 look valid.
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