### Fun Facts (Hints)

Mathematics has an extensive history in just about every culture or civilized society known to man. Listed below are some cool facts to get those math juices flowing:
In 1852 mathematician JJ Sylvester established the "theory of algebraic invariants."
In 1995 math great Andrew Wiles, proved "Fermat's Last Theorem."
The first decimal number system is said to have been invented in Ancient Egypt around 5000BC.
The Ancient Mayan civilization located in Central America is one of the only cultures in the recorded history of the world to use a place-value number system.
The American Mathematical Society was formed in the late months of 1888 in New York.

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Riddles and Answers © 2023

## Age Of Three Daughters Riddles

I was visiting a friend one evening and remembered that he had three daughters. I asked him how old they were. The product of their ages is 72, he answered. Quizzically, I asked, Is there anything else you can tell me? Yes, he replied, the sum of their ages is equal to the number of my house. I stepped outside to see what the house number was. Upon returning inside, I said to my host, Im sorry, but I still cant figure out their ages. He responded apologetically, Im sorry, I forgot to mention that my oldest daughter likes strawberry shortcake. With this information, I was able to determine all three of their ages. How old is each daughter?

Hint:

3, 3, and 8. The only groups of 3 factors of 72 to have non-unique sums are 2 6 6 and 3 3 8 (with a sum of 14). The rest have unique sums:

2 + 2 + 18 = 22

2 + 3 + 12 = 18

2 + 4 + 9 = 15

3 + 4 + 6 = 13

The house number alone would have identified any of these groups. Since more information was required, we know the sum left the answer unknown. The presence of a single oldest child eliminates 2 6 6, leaving 3 3 8 as the only possible answer.

YES NO

2 + 2 + 18 = 22

2 + 3 + 12 = 18

2 + 4 + 9 = 15

3 + 4 + 6 = 13

The house number alone would have identified any of these groups. Since more information was required, we know the sum left the answer unknown. The presence of a single oldest child eliminates 2 6 6, leaving 3 3 8 as the only possible answer.

*Did you answer this riddle correctly?*YES NO

## The Number Four Be Half Of Five Riddle

Hint:

IV, the Roman numeral for four, which is “half” (two letters) of the word five.

YES NO

*Did you answer this riddle correctly?*YES NO

## Bus Driver Riddle

Ok, you're the bus driver, there were 20 kids on the bus. At the first stop, 2 kids get on but 5 kids get off. The second stop, 3 kids get off but 1 gets on. The third stop, 8 kids get off but only 3 kids get off. Who's the bus driver?

Hint:

## Pearl Problems Riddle

"I'm a very rich man, so I've decided to give you some of my fortune. Do you see this bag? I have 5001 pearls inside it. 2501 of them are white, and 2500 of them are black. No, I am not racist. I'll let you take out any number of pearls from the bag without looking. If you take out the same number of black and white pearls, I will reward you with a number of gold bars equivalent to the number of pearls you took."

How many pearls should you take out to give yourself a good number of gold bars while still retaining a good chance of actually getting them?

How many pearls should you take out to give yourself a good number of gold bars while still retaining a good chance of actually getting them?

Hint: If you took out 2 pearls, you would have about a 50% chance of getting 2 gold bars. However, you can take even more pearls and still retain the 50% chance.

Take out 5000 pearls. If the remaining pearl is white, then you've won 5000 gold bars!

YES NO

*Did you answer this riddle correctly?*YES NO

## Coconut Toll Booth Riddle

There is a beautiful garden surrounded with water on three sides and only one road leading to it. This garden has thousands of coconut trees. Anyone can visit to pick coconuts.

The coconuts can be taken in boxes only. Each box can carry 20 coconuts.You can take as many boxes as you like for free but there are ten toll barriers on the road. Each toll booth collects tax in the form of you guessed it: coconuts. The number of coconuts taken is equal to the number of boxes. For example if you are carrying 50 boxes of coconut you have to pay 50 coconuts at each barrier.

If you took 10 boxes filled with coconuts from garden, tell me how many coconuts would you have remaining after crossing all ten toll booths?

The coconuts can be taken in boxes only. Each box can carry 20 coconuts.You can take as many boxes as you like for free but there are ten toll barriers on the road. Each toll booth collects tax in the form of you guessed it: coconuts. The number of coconuts taken is equal to the number of boxes. For example if you are carrying 50 boxes of coconut you have to pay 50 coconuts at each barrier.

If you took 10 boxes filled with coconuts from garden, tell me how many coconuts would you have remaining after crossing all ten toll booths?

Hint:

## Going To The Picnic

Mr and Mrs Smith went for a picnic. Mrs. Smith has 5 sons and each son has a sister who has 5 daughters each of whom have 1 brother each. How many of them went for the picnic?

Hint:

2 people.

It is stated clearly that Mr. and Mrs. Smith went for a picnic. It does not say that the others accompanied them.

YES NO

It is stated clearly that Mr. and Mrs. Smith went for a picnic. It does not say that the others accompanied them.

*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

## A Lady Steals $100

How smart are you?.....A lady walks in the store and steals $100 bill from the register without the owners knowledge. She comes back 5 mins later and buys $70 worth of goods with the $100 bill. The owner gives her $30 in change, how much did the owner lose????

A. $30

B. 70

C. $100

D. $130

E. $170

F. $200

DO NOT OVER THINK IT!

A. $30

B. 70

C. $100

D. $130

E. $170

F. $200

DO NOT OVER THINK IT!

Hint:

The best answer from the choices is the owner lost $100. The $100 bill that was stolen was then given back to the owner. What the owner loses is the $70 worth of goods and the $30 in change, which makes for a total of $70 + $30 = $100. The owner has lost $100.

Technically, the owner lost $30 plus the value, V, of the $70 of goods. Since stores typically sell goods at a markup, the value may be less than $70. But in the case of a loss leader, the owner may have lost more than $70.

YES NO

Technically, the owner lost $30 plus the value, V, of the $70 of goods. Since stores typically sell goods at a markup, the value may be less than $70. But in the case of a loss leader, the owner may have lost more than $70.

*Did you answer this riddle correctly?*YES NO

## 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

## 2 4 12 48 240 Riddle

Hint:

240. To get the number, multiply the previous number in the series by its position. 48 is in the 5th position, so 48 � 5 = 240

YES NO

*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

## Carton Of Eggs Riddle

There is a carton of 6 eggs on a table and there are 6 people round the table. Everybody takes an egg and there is still one in the carton. How is this possible?

Hint:

5 eggs are taken by the first 5 people, then the 6th person takes the egg , while its still in the carton!!

YES NO

*Did you answer this riddle correctly?*YES NO

## Finding The Angles

Hint:

47

Explanation:

At first look, it seems pretty easy but on the contrary, it is pretty tricky a question. So let us simplify it by dividing the triangle into three equal triangles (the triangles so formed if outer side is connected to the center of the circle) and then count the number of triangles in each part by taking two or more parts together.

First, let us take the triangles in one part. There are 4 non-overlapping and 3 overlapping triangles.

4 + 3 = 7

7 * 3 = 21

Next, if we take number of triangles by taking two parts together, there are 8 in total.

8 * 3 = 24

Lastly, the number of triangles if all three parts are taken together, there are a total of 2.

21 + 24 + 2 = 47.

YES NO

Explanation:

At first look, it seems pretty easy but on the contrary, it is pretty tricky a question. So let us simplify it by dividing the triangle into three equal triangles (the triangles so formed if outer side is connected to the center of the circle) and then count the number of triangles in each part by taking two or more parts together.

First, let us take the triangles in one part. There are 4 non-overlapping and 3 overlapping triangles.

4 + 3 = 7

7 * 3 = 21

Next, if we take number of triangles by taking two parts together, there are 8 in total.

8 * 3 = 24

Lastly, the number of triangles if all three parts are taken together, there are a total of 2.

21 + 24 + 2 = 47.

*Did you answer this riddle correctly?*YES NO

## Finding The Value Riddle

Can you solve the equation by finding the value of

1. Horse

2. Cowboy boot

3. Horseshoe

4. The last equation.

1. Horse

2. Cowboy boot

3. Horseshoe

4. The last equation.

Hint:

Horse = 10

Cowboy-Boot = 1

HorseShoe= 2

The Last equation = 21

Detailed Explanation :

Equation1:

3Horse = 30

=> Horse = 10 .....(1)

Equation2:

1Horse + 2HorseShoe + 2HorseShoe = 18

10 + 4HorseShoe =18

HorseShoe = 2 .....(3)

Equation3:

2HorseShoe - 2Cowboy-Boot = 2

4 - 2Cowboy-Boot = 2

=> Cowboy-Boot = 1 ... (2)

Equation4:

Cowboy-Boot+Horse*HorseShoe = 1+10*2

=>21

YES NO

Cowboy-Boot = 1

HorseShoe= 2

The Last equation = 21

Detailed Explanation :

Equation1:

3Horse = 30

=> Horse = 10 .....(1)

Equation2:

1Horse + 2HorseShoe + 2HorseShoe = 18

10 + 4HorseShoe =18

HorseShoe = 2 .....(3)

Equation3:

2HorseShoe - 2Cowboy-Boot = 2

4 - 2Cowboy-Boot = 2

=> Cowboy-Boot = 1 ... (2)

Equation4:

Cowboy-Boot+Horse*HorseShoe = 1+10*2

=>21

*Did you answer this riddle correctly?*YES NO

## Joe's 10 Coins Riddle

Joe has ten coins totaling $1.19. From these coins, he cannot make exact change for a dollar, half-dollar, quarter, dime, or nickel.

What are the coins?

What are the coins?

Hint:

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