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.
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).
Direct Link: www.brainbashers.com?ZBVT
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.
Which of the six black shapes is identical to the red one?
There may be more than one that is exactly the same.
The second group of trainee astronauts are all sitting around the table, waiting to start their first day of training.
From the clues given below, can work out where everyone sits?
Note: Seat 1 is next to Seat 2 and Seat 8, etc. Seat 5 is across from Seat 1, and Seat 7 is across from Seat 3, etc. Seat 2 is a higher seat number that Seat 1, etc.
1. Harvey has a higher seat number than Jennie.
2. Peter is across from Harvey.
3. Neither Joyce nor Lia is in seat 8.
4. Rick is across from Kenny, and Rick is also next to Joyce.
5. Lia is next to Kenny.
6. Jennie is at Seat 4 and next to Harvey.
7. Peter is next to Lia.
8. Mark has the remaining seat.
Seat 1 Peter
Seat 2 Lia
Seat 3 Kenny
Seat 4 Jennie
Seat 5 Harvey
Seat 6 Joyce
Seat 7 Rick
Seat 8 Mark
Jennie is in Seat 4 and next to Harvey (Clue 6), so Harvey is in Seat 3 or Seat 5.
Harvey has a higher seat number than Jennie (Clue 1), so Harvey is in Seat 5.
Peter is across from Harvey (Clue 2), so is in Seat 1.
Peter is next to Lia (Clue 7), so Lia is in Seat 8 or Seat 2. But Lia is not in Seat 8 (Clue 3), therefore Lia is in Seat 2.
Lia is next to Kenny (Clue 5), therefore Kenny must be in Seat 3.
Rick is across from Kenny (Clue 4), so must be in Seat 7.
Joyce is next to Rick (Clue 4), but not in Seat 8 (Clue 3), so Joyce must be in Seat 6.
The last remaining seat (Seat 8) is occupied by Mark (Clue 8).