### Fun Facts (Hints)

Different types of riddles have challenged people for centuries, here are a few facts about them that may give you some hints in solving these challenging questions:
Riddles in math are used by math teachers in many different cultures.
Many teachers promote the idea that giving students mathematical riddles helps to encourage their pupils to think more creatively and strategically.
These riddles are considered especially helpful in classrooms where students have emotional problems, as it pulls them away from their problems, and forces them to think creatively about what is before them.
Detectives are sometimes forced to solve riddles involving math when searching for psychopaths and serial killers.
Math riddles are used at home by many parents seeking to help their students become more engaged in their math schoolwork/homework.

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Riddles and Answers © 2021

## The Sad Math Book

Hint:

## 10 From 100 Riddle

Hint:

## Little Billy's Calculator

Little Billy has a calculator with 15 buttons. He has 10 keys for 0-9, a key for addition, multiplication, division, and subtraction. Finally, he has an = sign. However, Mark the Meanie messed up the programming on Billy's calculator. Now, whenever Billy presses any of the number keys, it comes up with a random single-digit number. The same goes for the four operations keys (+,-,x, /). So whenever Billy tries to press the + button, the calculator chooses randomly between addition, multiplication, subtraction, and division. The only key left untouched was the = sign.

Now, if Billy were to press one number key, one operation key, then another number key, then the = button, what are the chances the answer comes out to 6?

Now, if Billy were to press one number key, one operation key, then another number key, then the = button, what are the chances the answer comes out to 6?

Hint: Think about how many ways he could possibly get 6.

There is a 4% chance.

There are 16 possible ways to get 6.

0+6

1+5

2+4

3+3

6+0

5+1

4+2

9-3

8-2

7-1

6-0

1x6

2x3

6x1

3x2

6/1

There are 400 possible button combinations.

When Billy presses any number key, there are 10 possibilities; when he presses any operation key, there are 4 possibilities.

10(1st#)x4(Operation)x10(2nd#)=400

16 working combinations/400 possible combinations= .04 or 4%

YES NO

There are 16 possible ways to get 6.

0+6

1+5

2+4

3+3

6+0

5+1

4+2

9-3

8-2

7-1

6-0

1x6

2x3

6x1

3x2

6/1

There are 400 possible button combinations.

When Billy presses any number key, there are 10 possibilities; when he presses any operation key, there are 4 possibilities.

10(1st#)x4(Operation)x10(2nd#)=400

16 working combinations/400 possible combinations= .04 or 4%

*Did you answer this riddle correctly?*YES NO

## The Gardners Riddle

Gretchen and Henry were discussing their new neighbors, the Gardners. Gretchen mentioned that she met two of the daughters, and they each had blond hair.

"I have met all of the sisters," replied Henry, "and the probability that both of the girls you met would have had blond hair, assuming you were equally likely to meet any of the sisters, is exactly 50%. Do you know how many children there are?"

After thinking for a minute, Gretchen asks if the family is abnormally large. When Henry replies that it is not, Gretchen tells him how many girls are in the family. What number did she say?

"I have met all of the sisters," replied Henry, "and the probability that both of the girls you met would have had blond hair, assuming you were equally likely to meet any of the sisters, is exactly 50%. Do you know how many children there are?"

After thinking for a minute, Gretchen asks if the family is abnormally large. When Henry replies that it is not, Gretchen tells him how many girls are in the family. What number did she say?

Hint:

Gretchen said that there were 4 girls in the family, three of whom were blond.

This would make the probability that she saw two blonds (3/4) * (2/3), which equals 1/2.

Other numbers would work, but the next pair would lead to a rather large family.

YES NO

This would make the probability that she saw two blonds (3/4) * (2/3), which equals 1/2.

Other numbers would work, but the next pair would lead to a rather large family.

*Did you answer this riddle correctly?*YES NO

## 1 + 1 = 3 Riddle

Hint:

## 30 Sacks Of Coconuts

An intelligent trader travels from one place to another with 3 sacks having 30 coconuts each. No sack can hold more than 30 coconuts. On the way, he passes 30 check points. At each check point, he has to give one coconut for every sack he is carrying. What is the maximum number of coconuts that he can have with him at the end of his journey?

Hint:

He will have 25 coconuts with him at the end. The trick is to reduce the number of sacks as you pass checkpoints.

The first 10 checkpoints require 3 coconuts each, which empties his first sack. The next 15 checkpoints require 2 coconuts each, which will empty his second stack. Now, he is left with 1 sack and 5 more checkpoints. So, the 5 checkpoints will take 1 coconut each. Therefore, he will be left with 25 coconuts.

YES NO

The first 10 checkpoints require 3 coconuts each, which empties his first sack. The next 15 checkpoints require 2 coconuts each, which will empty his second stack. Now, he is left with 1 sack and 5 more checkpoints. So, the 5 checkpoints will take 1 coconut each. Therefore, he will be left with 25 coconuts.

*Did you answer this riddle correctly?*YES NO

## 100 Fruits

For $1 you get 40 Cherries. For $3 you get 1 Orange. For $5 you get 1 Watermelon. Your mother told you to get 100 fruits for $100. How many of Cherries, Oranges and Watermelons will you buy?

Hint:

## 5+5+5=550 Riddle

Hint:

## Equals Eight Riddle

Hint:

Mirror one of the threes and put it and the other three together to get an eight.

YES NO

*Did you answer this riddle correctly?*YES NO

## More Than 90 Degrees Riddle

Hint:

## Find The Digits Riddle

In the number wheel in the picture, you can find several digits except one question mark.

Can you find the digit that should be placed in place of that question mark?

Can you find the digit that should be placed in place of that question mark?

Hint:

The required digit is 0.

If you add up all the digits in any diagonal, you will find the sum to be 25.

YES NO

If you add up all the digits in any diagonal, you will find the sum to be 25.

*Did you answer this riddle correctly?*YES NO

## Apricot Jam Riddle

Morgan was making apricot jam. She put all the apricots in the pot and stirred them up. Then she remembered she had to add 1 ounce of lemon juice for every two apricots! How did she figure out how much lemon juice to put?

Hint:

## Bat And Ball Riddle

If a baseball and a bat cost $1.10 together, and the bat costs $1.00 more than the ball, how much does the ball cost?

Hint: The answer isn't 10 cents.

Here's the solution:

Although $1.00 + $0.10 does equal $1.10, if you take $1.00 $0.10 you get $0.90, but the problem requires that the bat costs $1 more than the ball.

So, the ball must cost $0.05, and the bat must cost $1.05 since $1.05 + $0.05 = $1.10

---

Still not convinced? You can use algebra to solve the problem:

First, lets set up the equation:

x + ($1.00 + x) = $1.10

$1.00 + 2x = $1.10

2x = $1.10 $1.00

2x = $0.101

Finally, solve for x:

x = $0.05

Check your work:

x + ($1.00 + x) = $1.10, so

$0.05 + ($1.00 + $0.05) = $1.10

YES NO

Although $1.00 + $0.10 does equal $1.10, if you take $1.00 $0.10 you get $0.90, but the problem requires that the bat costs $1 more than the ball.

So, the ball must cost $0.05, and the bat must cost $1.05 since $1.05 + $0.05 = $1.10

---

Still not convinced? You can use algebra to solve the problem:

First, lets set up the equation:

x + ($1.00 + x) = $1.10

$1.00 + 2x = $1.10

2x = $1.10 $1.00

2x = $0.101

Finally, solve for x:

x = $0.05

Check your work:

x + ($1.00 + x) = $1.10, so

$0.05 + ($1.00 + $0.05) = $1.10

*Did you answer this riddle correctly?*YES NO

## King Arthur's Round Table Riddle

Hint:

## Mathematical Warfare Riddle

Hint:

## Post Your Math Riddles Below

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