### Fun Facts (Hints)

Hard riddles are universal, and continue to leave a lasting impression on many different cultures across the globe. Here are some interesting facts:
The mere definition of what a riddle is, is something that has drawn a large amount of debate between scholars for centuries.
Complex riddles have been used since ancient times, and extensively in ancient/medieval literature.
There is only one riddle in the Bible appearing in the book of Judges. It is known as "Samson's riddle."
Charades is a popular contemporary game created with the use of riddle.
In author J. R. R. Tolkien's 'The Hobbit' Bilbo Baggins is given a challenging riddle by Gollum, and his life was dependent upon getting the correct answer.

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## An Island That Has 3 Gods

There is an Island that has 3 gods. One god always tells a lie, and the other always tells the truth. The third god has a random behavior. To top it off, these three gods, being jerks, answer in their own languages such that you are unable to tell which word, between "ja" or "da", means "no" or "yes". You have 3 questions to work out the True god, the false god, and the Random god.

Hint:

Question 1: (To any of the three gods) If I were to ask you "Is that the random god," would your answer be "ja?" (This questions, no matter the answer, will enable you to tell which god is not random i.e. the god who is either False or True)

Question 2: (To either the True or False god) If I asked you "are you false," would your answer be "ja?"

Question 3: (To the same god you asked the second question) If I asked you "whether the first god I spoke to is random," would your answer be "ja?"

YES NO

Question 2: (To either the True or False god) If I asked you "are you false," would your answer be "ja?"

Question 3: (To the same god you asked the second question) If I asked you "whether the first god I spoke to is random," would your answer be "ja?"

*Did you answer this riddle correctly?*YES NO

## Fooled By Thunder

Hint:

## Under The Cup Riddle

You decide to play a game with your friend where your friend places a coin under one of three cups. Your friend would then switch the positions of two of the cups several times so that the coin under one of the cups moves with the cup it is under. You would then select the cup that you think the coin is under. If you won, you would receive the coin, but if you lost, you would have to pay.

As the game starts, you realise that you are really tired, and you don't focus very well on the moving of the cups. When your friend stops moving the cups and asks you where the coin is, you only remember a few things:

He put the coin in the rightmost cup at the start.

He switched two of the cups 3 times.

The first time he switched two of the cups, the rightmost one was switched with another.

The second time he switched two of the cups, the rightmost one was not touched.

The third and last time he switched two of the cups, the rightmost one was switched with another.

You don't want to end up paying your friend, so, using your head, you try to work out which cup is most likely to hold the coin, using the information you remember.

Which cup is most likely to hold the coin?

As the game starts, you realise that you are really tired, and you don't focus very well on the moving of the cups. When your friend stops moving the cups and asks you where the coin is, you only remember a few things:

He put the coin in the rightmost cup at the start.

He switched two of the cups 3 times.

The first time he switched two of the cups, the rightmost one was switched with another.

The second time he switched two of the cups, the rightmost one was not touched.

The third and last time he switched two of the cups, the rightmost one was switched with another.

You don't want to end up paying your friend, so, using your head, you try to work out which cup is most likely to hold the coin, using the information you remember.

Which cup is most likely to hold the coin?

Hint: Write down the possibilities. Remember that there are only three cups, so if the rightmost cup wasn't touched...

The rightmost cup.

The rightmost cup has a half chance of holding the coin, and the other cups have a quarter chance.

Pretend that Os represent cups, and Q represents the cup with the coin.

The game starts like this:

OOQ

Then your friend switches the rightmost cup with another, giving two possibilities, with equal chance:

OQO

QOO

Your friend then moves the cups again, but doesn't touch the rightmost cup. The only switch possible is with the leftmost cup and the middle cup. This gives two possibilities with equal chance:

QOO

OQO

Lastly, your friend switches the rightmost cup with another cup. If the first possibility shown above was true, there would be two possibilities, with equal chance:

OOQ

QOO

If the second possibility shown above (In the second switch) was true, there would be two possibilities with equal chance:

OOQ

OQO

This means there are four possibilities altogether, with equal chance:

OOQ

QOO

OOQ

OQO

This means each possibility equals to a quarter chance, and because there are two possibilities with the rightmost cup having the coin, there is a half chance that the coin is there.

YES NO

The rightmost cup has a half chance of holding the coin, and the other cups have a quarter chance.

Pretend that Os represent cups, and Q represents the cup with the coin.

The game starts like this:

OOQ

Then your friend switches the rightmost cup with another, giving two possibilities, with equal chance:

OQO

QOO

Your friend then moves the cups again, but doesn't touch the rightmost cup. The only switch possible is with the leftmost cup and the middle cup. This gives two possibilities with equal chance:

QOO

OQO

Lastly, your friend switches the rightmost cup with another cup. If the first possibility shown above was true, there would be two possibilities, with equal chance:

OOQ

QOO

If the second possibility shown above (In the second switch) was true, there would be two possibilities with equal chance:

OOQ

OQO

This means there are four possibilities altogether, with equal chance:

OOQ

QOO

OOQ

OQO

This means each possibility equals to a quarter chance, and because there are two possibilities with the rightmost cup having the coin, there is a half chance that the coin is there.

*Did you answer this riddle correctly?*YES NO

## Dropping Coconuts Riddle

You have two coconuts and you want to find out how high they can be dropped from a 100 story building before they break. But you only have $1.40 and the elevator costs a dime each time you ride it up (it's free for rides down).

How can you drop the coconuts to guarantee you will find the lowest floor they will break at, while starting and ending at floor 1?

How can you drop the coconuts to guarantee you will find the lowest floor they will break at, while starting and ending at floor 1?

Hint: They break when dropped from the same height and they don't weaken from getting dropped.

You could drop it at floor 1 first (because you start at floor 1). Then you would go to the floors: 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99, and 100. Whatever floor your first coconut breaks at, go to the floor above the last floor the coconut survived and drop the second coconut from this floor. Then go up by one floor until the second coconut breaks and that is the lowest floor it will break at.

YES NO

*Did you answer this riddle correctly?*YES NO

## Coconut Sentence Riddle

Hint: Listen closely...

This.

If 'this' is a coconut, and 'that' is a coconut, then 'is' 'this' a coconut.

YES NO

If 'this' is a coconut, and 'that' is a coconut, then 'is' 'this' a coconut.

*Did you answer this riddle correctly?*YES NO

## The Weight Of A Melon Riddle

Watermelon is 99% water. I have 100 pounds of watermelon. After a week, drying in the sun, the shriveled watermelon had only dried down to being 98% water. What is the total weight of the watermelon now?

Hint: We are to determine X the total mass of melon after the drying.
The Dry weight, DW is 1lb both before and after the drying.
The New Water weight, WNW is clearly X - DW or X - 1

## Give Me Food And I Will Live Give Me Water And I Will Die

Hint:

## Prince Age Riddle

A princess is as old as the prince will be when the princess is twice the age that the prince was when the princess's age was half the sum of their present ages.

What are their ages?

What are their ages?

Hint:

Current Future Past

Princess x 2z (x+y)/2

Prince y x z

I then created three equations, since the difference in their age will always be the same.

d = the difference in ages

x y = d

2z x = d

x/2 + y/2 z = d

I then created a matrix and solved it using row reduction.

x y z

1 -1 0 d

-1 0 2 d

.5 .5 -1 d

It reduced to:

x y z

1 0 0 4d

0 1 0 3d

0 0 1 5d/2

This means that you can pick any difference you want (an even one presumably because you want integer ages).

Princess age: 4d

Prince age: 3d

Ages that work

Princess:

4

8

16

24

32

40

48

56

64

72

80

Prince:

3

6

12

18

24

30

36

42

48

54

60

YES NO

Princess x 2z (x+y)/2

Prince y x z

I then created three equations, since the difference in their age will always be the same.

d = the difference in ages

x y = d

2z x = d

x/2 + y/2 z = d

I then created a matrix and solved it using row reduction.

x y z

1 -1 0 d

-1 0 2 d

.5 .5 -1 d

It reduced to:

x y z

1 0 0 4d

0 1 0 3d

0 0 1 5d/2

This means that you can pick any difference you want (an even one presumably because you want integer ages).

Princess age: 4d

Prince age: 3d

Ages that work

Princess:

4

8

16

24

32

40

48

56

64

72

80

Prince:

3

6

12

18

24

30

36

42

48

54

60

*Did you answer this riddle correctly?*YES NO

## Missing Dollar Riddle

Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself. Each guest got $1 back: so now each guest only paid $9; bringing the total paid to $27. The bellhop has $2. And $27 + $2 = $29 so, if the guests originally handed over $30, what happened to the remaining $1?

Hint: Make a list of all of the people involved and how much money they ended up with/spent.

The $9 paid by each guest accounts for the $2 that went to the bellhop. So rather than adding $27 to the $2 kept by the bellhop, the $27 accounts for the bellhops money. The $27 plus the $3 kept by the guests does add up to $30.

YES NO

*Did you answer this riddle correctly?*YES NO

## Rope Burn Riddle

You have two ropes. Each rope takes one hour to burn. These ropes are not identical, nor are they uniform; i.e. it does not necessarily take half an hour for half the rope to burn (if you have trouble visualizing this, imagine a rope of varying thickness across its length). With only these two ropes and a way to light them, how do you measure out 45 minutes?

Hint: You can light multiple ends and/or multiple ropes at the exact same time.

Light both ends of one rope, and only one end of the other rope. This will cause the first rope to burn out in 30 minutes. When the first rope burns out, there will be 30 minutes left on the second rope. So then, light the other end of the second rope, and the rest of it will burn out in 15 minutes. 30 + 15 = 45 minutes.

YES NO

*Did you answer this riddle correctly?*YES NO

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