## Puzzle 5

My first is in bridge, but not in ridge.

My second is in awake, and in mistake.

My third is in danger, but not in ranger.

My fourth is in strange, and in orange.

My fifth is in spline, and in nine.

My last is in river, and in diver.

My whole likes the darkness.

What am I?

Puzzle Copyright © Kevin Stone

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Hint

The first letter can only be B.

Answer

A badger.

Reasoning

My first is in bridge, but not in ridge = **B**

My second is in awake, and in mistake = **A** K E

My third is in danger, but not in ranger = **D**

My fourth is in strange, and in orange = R A N **G** E

My fifth is in spline, and in nine = I N **E**

My last is in river, and in diver = **R** I V E

## Puzzle 6

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 × 12 = 3672

If all of the people were children, then three quarters of them (459) would be given 8 sweets:

459 × 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 × 12 + 75 × 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 × 12 sweets = ^{3}/_{4} children × 8 sweets (both are 6).

## 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[----]room
quarter[----]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

Puzzle Copyright © Kevin Stone

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Hint

The first letters of the words are: w, w, s, y, b, b, s, l, s, f.

Answer

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

## Puzzle 8

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.

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