Puzzle 21
A kind old person decided to give 12 sweets to each of the adults in the town, and 8 sweets to each of the children.
Of the 612 people in the town, exactly half of the adults, and exactly three quarters of the children took the sweets.
How many sweets did the kind old person have to buy?
Puzzle Copyright © Kevin Stone
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Hint
The number of adults and children doesn't 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).
Puzzle 22
How many hexagon-type shapes, in total, can you find in this puzzle?
Puzzle Copyright © Kevin Stone
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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.
Puzzle 23
A large fresh water reservoir has two types of drainage system: small pipes and large pipes.
6 large pipes, on their own, can drain the reservoir in 12 hours.
3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours.
How long will 5 small pipes, on their own, take to drain the reservoir?
Puzzle Copyright © Kevin Stone
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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.
Puzzle 24
A very long time ago, at the beginning of the week, I was given some money for my birthday.
On Monday, I spent a quarter of the money on clothes.
On Tuesday, I spent one third of the remaining money on music.
On Wednesday, I spent half of the remaining money on food.
Finally, on Thursday, I spent the last £1.25 on a book.
How much birthday money did I receive?
Puzzle Copyright © Kevin Stone
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Hint
It might be easier to work backwards.
Answer
£5.00.
Reasoning
Working backwards:
On Thursday, I had £1.25.
On Wednesday, I had £1.25 x (1 ÷ one half) = £2.50.
On Tuesday, I had £2.50 x (1 ÷ two thirds) = £3.75.
On Monday, I had £3.75 x (1 ÷ three quarters) = £5.00.
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