THE CLUB CLOCK.—solution

The positions of the hands shown in the illustration could only indicate that the clock stopped at 44 min. 51¹¹⁴³/₁₄₂₇ sec. after eleven o'clock. The second hand would next be "exactly midway between the other two hands" at 45 min. 52⁴⁹⁶/₁₄₂₇ 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. 22¹⁰⁶/₁₄₂₇ 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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