# Riddles: A Baker's Dozen That Tests Your Reasoning Skills

I have been teaching mathematics in an Australian High School since 1982, and I am a contributing author to mathematics text books.

With the benefit of hindsight, you nod your head sagely in understanding a given solution to a riddle in a puzzle book. However, the next question stumps you, and the question after that, ad nauseam. This is because we all have our prejudices that filter through to our day-to-day activities. If I stated that my friend is a bouncer at a nightclub, your first instinctive impression is that my friend is male. When I buy meat and a friend asks, “where did you get it from?”, my immediate thought is that there is something wrong with it.

I recall as a student doing a test whose first instruction was to read every question and instruction before writing. As there were fifty questions spread over several pages, I feverishly began to write answers, finally -and with satisfaction- reaching the last question on the last page an hour later.

However, as I was about to read the last question, I glanced at the bottom of the page and saw written:

'Do not write answers to any question. Remain quiet for the lesson and hand in your empty test to the teacher.'

With this sobering thought, what follows is a presentation of some riddles, with solutions, that require you to be totally objective, to think ‘outside the box’ and not to accept things on face value.

So, sit back, shed your biases and enjoy the offerings.

## #1. Who is it?

Joe points to a picture and states:

"Brothers and sisters I have none,

But that man's father is my father's son."

Who is Joe referring to?

Discussion

“My father’s son” refers to Joe or a brother, but Joe does not have brothers.

Hence, 'my father's son' is Joe.

The third line can now be stated as, "That man's father is Joe."

Therefore, the person in the portrait is Joe's son.

The reference to having no sisters is a red herring. It is irrelevant.

## #2. Which farm to use?

Farmer John and farmer Jim share a common fence. Exactly on that fence is a tall tree on which squirrels live happily. One day, a storm shakes the tree and some squirrels fall to the ground, with all but four surviving.

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On whose side of the fence should the surviving squirrels be buried?

Discussion

The key phrase here is ‘surviving animals’.

Surely, we hope that neither Farmer John nor Farmer Jim is callous to the point of wanting to inter the distressed live squirrels. These critters should be allowed to collect their supply of acorns to see out the next storm.

## #3. In which direction is the smoke?

A diesel train leaves the town of Happyville and travels north. Soon, it reaches a speed of 80 kilometres/hour, even though there is a strong westerly wind blowing.

In which direction is the smoke drifting?

Discussion

Before you begin to use vectors, protractors and graph paper to calculate the wind direction, consider the meaning of “diesel train”.

A diesel engine uses diesel fuel. It does not produce smoke, no matter how hard the train driver might try by locking the brakes or attempting to perform “burn outs” in an effort to capture the rebellion of his youth.

## #4. Where does the egg fall?

A rooster resting at the top of a sloping roof lays an egg.

On which side of the roof-line will the egg roll?

Discussion

I am all for equality of the sexes, but even I would stop short of demanding that a rooster lay an egg. If there were such a thing, it would be tantamount to ‘the goose that lays the golden egg’.

## #5. Which direction to walk?

Where on Earth must you be so that regardless of your initial direction, you will always be moving south?

Discussion

Do you feel like a geography lesson? Meridians of longitude are imaginary lines that run from the north of the earth down to the south of the earth. Their number is infinite, so imagine starting at the north pole. Take one step forward in any direction and you will find yourself following one of these meridians of longitude southbound.

## #6. How fast do you fall?

Suppose there is a hole at the surface of Earth that passes through its centre and through to the other side.

Ignoring issues such as heat, friction and collision, if you jump into the hole, at what speed will you exit at the other end?

Discussion

You fall into the hole at one end and accelerate "downward" until you reach the earth's centre.

As you pass the centre, your orientation is now "upward", and the force of gravity makes you decelerate as you make your way towards the earth's surface at the other end.

At the point of reaching the surface, your acceleration and speed is zero.

## #7. Dig half a hole

Tim and Bjorn are digging holes to hold fence posts.

Tim takes 20 minutes to dig a hole to a depth of 1.2 metres and Bjorn takes 25 minutes to dig a hole of the same size.

If both start at the same time, who will be the fastest to dig half a hole?

Discussion

Let’s suppose we are looking at a hole 2 metres deep. If we fill it with sand until it is 1 metre deep, does that mean we now have half a hole?

Clearly, saying “half a hole” is as nonsensical as claiming that a woman is “half pregnant”.

What is wrong with this statement?

“I’d give my right arm to be ambidextrous!”

Discussion

To be ambidextrous means to be able to use both hands equally well.

If you suddenly find yourself minus your right arm, it may be a tad difficult to satisfy the definition of ambidextrous.

## #9. Where is the surgeon?

The father and mother of a patient are in a hospital room.

The surgeon says that medical ethics forbids a surgeon to operate on a family member.

The father and mother leave the room, which is now empty.

There is no other exit to the room.

Discussion

No, the surgeon did not disappear in a puff of smoke.

Did you assume that there were three people in the room, the husband, the wife and the surgeon?

Is it possible that there were only two? What if either the husband or the wife were the surgeon?

## #10. How do you exit the forest?

You are in the middle of a forest. You do not have a compass, but that doesn’t matter because you know that if you walk in a straight line in any direction, you will reach the exit in the same amount of time as taking any other direction.

How is this possible?

Discussion

We’ve had a geography lesson in our discussion to a previous question, so what about a lesson in geometry?

If you are standing in the middle of a circle, your distance, called the radius, to any point on the circumference of the circle is the same.

This means the forest must be circular in shape, and you are standing at its centre.

## #11. Thank you!

A woman walks to the counter of a bar and asks for a glass of water.

Instead, the barman takes out a gun and shoots her.

The woman says, “Thank you” and leaves.

Why was the barman thanked?

Discussion

An old wives’ tale has it that drinking water in a variety of interesting ways, such as holding your nose or upside down, will stop you hiccupping.

Another tale just as spurious is that a sudden fright will achieve similar results.

Does pointing a gun at someone (obviously a prop gun) and firing qualify as a ‘hiccup cure”?

## #12. It's cold in here.

Doug, an evil person, imprisons Tom in a freezer store room. The room is empty except for the actual freezer section where fruit is kept at below zero temperature by blocks of ice.

There is a detachable skylight at the top of the four-metre high ceiling.

Before he leaves, Dough feels some sympathy for Tom and increases the temperature.

Upon his return next morning, Doug opens the securely locked door and finds the freezer empty. There is no sign of a forced exit, and the only thing to be seen is a pool of water on the concrete floor.

How did Tom escape?

Discussion

Tom cannot reach the skylight without assistance. There are blocks of ice in the freezer. Stacked in the form of steps, they fuse together, and Tom might be able to climb up and secure his freedom through the skylight.

We know that ice melts. By next morning, the ice would have melted, leaving only a puddle where the improvised ladder had been.

## #13. A cat's tale.

John and Betty are found dead on the floor of the lounge room. The cat, with wet fur, was nearby, calmly grooming itself amongst broken glass.

The police immediately concluded that the deaths of John and Betty was due to asphyxiation.

How were the police so sure of the cause of death without further enquiry?

Discussion

Can we assume that John and Betty are the unfortunate human husband and wife who tragically died from asphyxiation in the lounge room of their home?

Cats are temperamental and possessive creatures. Do they like fish?

What would a cat try to do if it saw a pair of attractive goldfish swimming in a glass fish bowl that sat on the benchtop?

A possible scenario is that John and Betty were the names of the goldfish. The cat, for reasons known only to cats, decided to taunt the fish by placing its paw inside the bowl.

In an act of frustration, it placed both paws in the bowl and the fishbowl toppled over the side, with some of the water spraying the cat. The bowl hit the floor and broke, thus condemning the fish to their undeserved demise.

• What is wrong in saying “A drake laid an egg”?
• You walk 1 km, then ½ km, then ¼ km, and so on. Will your total distance reach 2 km?
• Is it possible to find a coin dated 5 BCE?
• Explain how it is possible to have two mothers and two daughters when there are only three people.
• Why don’t people living at the North Pole or South Pole catch colds?