We were told that the bullet that killed Mr. Stanton Mowbray struck the
very centre of the clock face and instantly welded together the hour,
minute, and second hands, so that all revolved in one piece. The puzzle
was to tell from the fixed relative positions of the three hands the
exact time when the pistol was fired.
We were also told, and the illustration of the clock face bore out the
statement, that the hour and minute hands were exactly twenty divisions
apart, "the third of the circumference of the dial." Now, there are
eleven times in twelve hours when the hour hand is exactly twenty
divisions ahead of the minute hand, and eleven times when the minute hand
is exactly twenty divisions ahead of the hour hand. The illustration
showed that we had only to consider the former case. If we start at four
o'clock, and keep on adding 1 h. 5 m. 27-3/11 sec., we shall get all
these eleven times, the last being 2 h. 54 min. 32-8/11 sec. Another
addition brings us back to four o'clock. If we now examine the clock
face, we shall find that the seconds hand is nearly twenty-two divisions
behind the minute hand, and if we look at all our eleven times we shall
find that only in the last case given above is the seconds hand at this
distance. Therefore the shot must have been fired at 2 h. 54 min. 32-8/11
sec. exactly, or, put the other way, at 5 min. 27-3/11 sec. to three
o'clock. This is the correct and only possible answer to the puzzle.