Brain Teasers and Puzzles 

Workings

Hint
The first letters of the words are: W, W, S, Y, B, B, S, L, S, F.

Answers
  drift[wood]wind    home[work]bench    foot[step]mother   court[yard]stick    moth[ball]room quarter[back]ground   space[ship]yard    wild[life]span    your[self]less    back[fire]fighter

Workings

Hint
There are more than 37, look at the different sizes.

Answer
There are 64 hexagon-type shapes in total.

Reasoning
37 single hexagons
 + 19 hexagons that contain 7 smaller hexagons
 + 7 hexagons that contain 19 smaller hexagons
 + 1 large hexagon that contains all of the smaller hexagons.

Workings

Hint
There are over 20 mistakes.

Answer
21.

Reasoning
Many years ago, before modern education in the new millennium, one problem in schools was basic spelling and grammar. To combat this and raise achievement, teachers were advised to start at the very beginning, at the youngest age. Once they had managed to breathe new life into lessons, progress came quickly, success was then guaranteed. How many spelling errors would modern scholars identify in this passage?

Workings

Hint
How many large pipes are required to drain the reservoir in 24 hours?

Answer
21 hours and 36 minutes.

Reasoning
Looking at the first clue:
   in 12 hours, 6 large pipes can drain 1 reservoir
   in 24 hours, 6 large pipes can drain 2 reservoirs
   (*) in 24 hours, 3 large pipes can drain 1 reservoir

Looking at the second clue:
   in 8 hours, 3 large + 9 small pipes can drain 1 reservoir
   in 24 hours, 3 large + 9 small pipes can drain 3 reservoirs

But, by (*), we know that in those 24 hours, 3 large pipes can drain 1 of those reservoirs.

Therefore, the other 2 reservoirs can be drained by the small pipes on their own:
   in 24 hours, 9 small pipes can drain 2 reservoirs
   in 24 hours, 1 small pipe can drain 2/9 reservoirs
multiply the hours by 9:
   in 216 hours, 1 small pipe can drain 2 reservoirs
   in 216 hours, 5 small pipes can drain 10 reservoirs
divide the hours by 10:
   in 21.6 hours, 5 small pipes can drain 1 reservoir

21.6 hours = 21 hours and 36 minutes.