Hint
Does the number of adults and children matter?
Answer
3,672.
Reasoning
The actual number of adults and children doesn't actually matter.
If all of the people were adults, then half of them (306) would be given 12 sweets:
306 x 12 = 3672
If all of the people were children, then three quarters of them (459) would be given 8 sweets:
459 x 8 = 3672
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
We can change the numbers of adults and children, but it doesn't change the answer.
The reason for this lies in the fact that 1/2 adults x 12 sweets = 3/4 children x 8 sweets (both are 6).
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Puzzle 82
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
21.6 hours = 21 hours and 36 minutes.
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Puzzle 84
Below, 10 nine-letter words have been broken into chunks of three letters.
The chunks have been moved around, no chunk is used twice, and all of the chunks are used.
Can you determine what the 10 words are?
cer ent ead rat uti spr
ful oun pro ann ope ock
nce een oat est liv ion
nou sev ion ast hou akf
bre bea ens dim bed seb
Hint
The first letters of the words are: P, B, D, L, O, A, B, H, S, B.
Answers
pro + nou + nce = pronounce
bea + uti + ful = beautiful
dim + ens + ion = dimension
liv + est + ock = livestock
ope + rat + ion = operation
ann + oun + cer = announcer
bed + spr + ead = bedspread
hou + seb + oat = houseboat
sev + ent + een = seventeen
bre + akf + ast = breakfast
