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I was having trouble sleeping last night and I tossed and turned well into the night.
Our local town hall has a clock which strikes on the hour and also strikes just once on the half hour.
During one of my more awake moments I heard the clock strike once, but I could not tell what time it was.
Half an hour later it struck once again, but I still could not tell what time it was.
Finally, half an hour later it struck once again and I knew what the time was.
What time was it?
[Ref: ZEQH]
Hint: When does the clock strike just once?
Answer: 1.30 in the morning.
The initial single strike was at 12.30.
Puzzle 18
Which country has been hidden in the paragraph below:
The local habitat around a railway track can be very interesting. For example, supporting the track is a sleeper, under which you can find the lesser spotted great weevil.
The local habitat around a railway track can be very interesting. For example, supporting the track is a sleeper, under which you can find the lesser spotted great weevil.
Puzzle 19
In the illustration we have a sketch of Sir Edwyn de Tudor going to rescue his love, who was held a captive by a neighbouring wicked baron.
Sir Edwyn calculated that if he rode at fifteen miles an hour he would arrive at the castle an hour too soon, while if he rode at ten miles an hour he would get there just an hour too late.
Now, it was of the first importance that he should arrive at the exact time appointed, in order that the rescue that he had planned should be a success, and the time of the tryst was five o'clock, when the captive would be taking afternoon tea.
The puzzle is to discover exactly how far Sir Edwyn de Tudor had to ride.
[Ref: ZBVT] Sir Edwyn De Tudor. From Amusements In Mathematics by Henry Ernest Dudeney (1917).
Hint: The gap between the two options is 2 hours.
Answer: The distance must have been sixty miles.
If Sir Edwyn left at noon and rode 15 miles an hour, he would arrive at four o'clock  an hour too soon. If he rode 10 miles an hour, he would arrive at six o'clock  an hour too late. But if he went at 12 miles an hour, he would reach the castle of the wicked baron exactly at five o'clock  the time appointed.
The text above is the answer given in the book, and below is a method of finding the answer.
If we call the distance to the castle, D and using the fact that Time = Distance ÷ Speed, we have:
Travelling at 15 mph:
Time1 = D ÷ 15 (an hour too soon)
Travelling at 10 mph:
Time2 = D ÷ 10 (an hour too late)
The time gap between these two times is 2 hours, therefore
Time2  Time1 = 2
D ÷ 10  D ÷ 15 = 2
Multiply throughout by 30:
3D  2D = 60
D = 60 miles.
Puzzle 20
Which of the six black shapes is identical to the red one?
There may be more than one that is exactly the same.
Hint: Try and rotate them around in your head, and watch out for mirror images.
Answer: A and C.
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