62.—­The club clock.

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?

[Illustration]

63.—­The stop-watch.

[Illustration]

We have here a stop-watch with three hands.  The second hand, which travels once round the face in a minute, is the one with the little ring at its end near the centre.  Our dial indicates the exact time when its owner stopped the watch.  You will notice that the three hands are nearly equidistant.  The hour and minute hands point to spots that are exactly a third of the circumference apart, but the second hand is a little too advanced.  An exact equidistance for the three hands is not possible.  Now, we want to know what the time will be when the three hands are next at exactly the same distances as shown from one another.  Can you state the time?

64.—­The three clocks.

On Friday, April 1, 1898, three new clocks were all set going precisely at the same time—­twelve noon.  At noon on the following day it was found that clock A had kept perfect time, that clock B had gained exactly one minute, and that clock C had lost exactly one minute.  Now, supposing that the clocks B and C had not been regulated, but all three allowed to go on as they had begun, and that they maintained the same rates of progress without stopping, on what date and at what time of day would all three pairs of hands again point at the same moment at twelve o’clock?

65.—­The railway station clock.

A clock hangs on the wall of a railway station, 71 ft. 9 in. long and 10 ft. 4 in. high.  Those are the dimensions of the wall, not of the clock!  While waiting for a train we noticed that the hands of the clock were pointing in opposite directions, and were parallel to one of the diagonals of the wall.  What was the exact time?

66.—­The village simpleton.

A facetious individual who was taking a long walk in the country came upon a yokel sitting on a stile.  As the gentleman was not quite sure of his road, he thought he would make inquiries of the local inhabitant; but at the first glance he jumped too hastily to the conclusion that he had dropped on the village idiot.  He therefore decided to test the fellow’s intelligence by first putting to him the simplest question he could think of, which was, “What day of the week is this, my good man?” The following is the smart answer that he received:—­

“When the day after to-morrow is yesterday, to-day will be as far from Sunday as to-day was from Sunday when the day before yesterday was to-morrow.”