Hint
Does the number of adults and children matter?
Answer
3,672.
Reasoning
The actual number of adults and children doesn't matter.
For example, if all of the people were adults, then half of them (306) would be given 12 sweets:
306 x 12 = 3672
For example, if all of the people were children, then three quarters of them (459) would be given 8 sweets:
459 x 8 = 3672
For example, if there were 512 adults (so 256 would get 12 sweets = 3072) and 100 children (so 75 would get 8 sweets = 600):
256 x 12 + 75 x 8 = 3672
As you can see, we can change the numbers of adults and children, and it doesn't change the answer.
The reason for this lies in the fact that 1⁄2 adults x 12 sweets
and 3⁄4 children x 8 sweets
both equal 6 sweets.
??
Puzzle 7
Can you place a different 4-letter word into each of the brackets to create two longer words? drift[----]wind home[----]bench foot[----]mother court[----]stick moth[----]roomquarter[----]ground space[----]yard wild[----]span your[----]less back[----]fighter
In the following example, the word 'book' creates the words 'cookbook' and 'bookcase'.
cook[book]case
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
