57.—­What was the time?

“I say, Rackbrane, what is the time?” an acquaintance asked our friend the professor the other day.  The answer was certainly curious.

“If you add one quarter of the time from noon till now to half the time from now till noon to-morrow, you will get the time exactly.”

What was the time of day when the professor spoke?

58.—­A time puzzle.

How many minutes is it until six o’clock if fifty minutes ago it was four times as many minutes past three o’clock?

59.—­A puzzling watch.

A friend pulled out his watch and said, “This watch of mine does not keep perfect time; I must have it seen to.  I have noticed that the minute hand and the hour hand are exactly together every sixty-five minutes.”  Does that watch gain or lose, and how much per hour?

60.—­The Wapshaw’s wharf mystery.

There was a great commotion in Lower Thames Street on the morning of January 12, 1887.  When the early members of the staff arrived at Wapshaw’s Wharf they found that the safe had been broken open, a considerable sum of money removed, and the offices left in great disorder.  The night watchman was nowhere to be found, but nobody who had been acquainted with him for one moment suspected him to be guilty of the robbery.  In this belief the proprietors were confirmed when, later in the day, they were informed that the poor fellow’s body had been picked up by the River Police.  Certain marks of violence pointed to the fact that he had been brutally attacked and thrown into the river.  A watch found in his pocket had stopped, as is invariably the case in such circumstances, and this was a valuable clue to the time of the outrage.  But a very stupid officer (and we invariably find one or two stupid individuals in the most intelligent bodies of men) had actually amused himself by turning the hands round and round, trying to set the watch going again.  After he had been severely reprimanded for this serious indiscretion, he was asked whether he could remember the time that was indicated by the watch when found.  He replied that he could not, but he recollected that the hour hand and minute hand were exactly together, one above the other, and the second hand had just passed the forty-ninth second.  More than this he could not remember.

What was the exact time at which the watchman’s watch stopped?  The watch is, of course, assumed to have been an accurate one.

61.—­Changing places.

[Illustration]

The above clock face indicates a little before 42 minutes past 4.  The hands will again point at exactly the same spots a little after 23 minutes past 8.  In fact, the hands will have changed places.  How many times do the hands of a clock change places between three o’clock p.m. and midnight?  And out of all the pairs of times indicated by these changes, what is the exact time when the minute hand will be nearest to the point ix?