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THE CLUB CLOCK.

(Money Puzzles)
One of the big clocks in the Cogitators' Club was found the other night
to have stopped just when, as will be seen in the illustration, the
second hand was exactly midway between the other two hands. One of the
members proposed to some of his friends that they should tell him the
exact time when (if the clock had not stopped) the second hand would
next again have been midway between the minute hand and the hour hand.
Can you find the correct time that it would happen?

The positions of the hands shown in the illustration could only indicate
that the clock stopped at 44 min. 51+1143/1427 sec. after eleven
o'clock. The second hand would next be "exactly midway between the other
two hands" at 45 min. 52+496/1427 sec. after eleven o'clock. If we had
been dealing with the points on the circle to which the three hands are
directed, the answer would be 45 min. 22+106/1427 sec. after eleven; but
the question applied to the hands, and the second hand would not be
between the others at that time, but outside them.

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