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## Not On My Watch

Inspector Lee looked once again in at the dead body of Horace Rimple and noted the time on the shattered watch: 1:10 pm. The watch had undoubtedly been shattered by the bullet which killed old Mr. Rimple as he lay asleep in his bed.

"Tell me what happened today," Lee instructed the butler.

"As always, on Sunday, it was Mr. Rimple's wish to have the family gather for the afternoon. On days such as today, when he was feeling unwell, the members of the family were to go in and sit by his bed to talk, even if he looked asleep. He could still hear them talk even if he did not make the effort to open his eyes."

"Today, as customary, Robert spent the time from 1:00 to 1:03 with him, Susan the time from 1:03 to 1:06, James the time from 1:06 to 1:09, William the time from 1:09 to 1:12; Lawrence the time from 1:12 to 1:15, and Mary the youngest the time from 1:15 to 1:18. Mr. Rimple was very particular about those times. Each of them said he seemed to be asleep."

"Well," said Inspector Lee, "It seems very clear that William is the murderer."

"Unfortunately," said the butler, "It is not quite that simple. While Mr. Ripple loved that old watch, it did not keep very good time. It lost exactly six minutes every 24 hours. I would set it correct every night at 11:00 before going to bed. thus, the watch was always incorrect after that."

"Ah," said Inspector Lee, "Then the murderer must be...."

Question: Who do you think is the murderer and why?

Source: S.D. (former student)

Hint: How much time did his watch lose every hour? Every four hours?

What is the actual time when Mr. Ripple's watch says 3 am for example?

Solution Commentary: S.D. provided this discussion: "Since the watch is set every night at 11:00 pm, it was 14 hours and 10 minutes later when Mr. Rimple was shot.

We can figure out that his watch lost 1 minute every 4 hours, 3 minutes lost every 12 hours, 1/2 minute lost in 2 hours, and 15 seconds lost in 1 hour.

Thus, if you take the 14 hours and 10 minutes, 4 hours three times = 4 minutes plus 1/2 minute for the other 2 hours remaining = 4 1/2 minutes added to the 1:10 equals 1:14 (and some odd seconds). So Lawrence is the murderer."

Note: S.D. made an error in her solution commentary...can you find it? Also, does the error change the identity of the murderer?