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## The Monty Hall Problem

You are on a game show in which there are three identical doors, one with a car behind it and two with goats behind them. You must pick one door, and you win if that door has the car behind it.

After you pick a door, the host of the game show always opens a door you didn’t choose that has a goat behind it. This leaves the door you chose and one other remaining door, and you are given the option to switch your choice to the other remaining door.

Should you switch or should you stick to your original choice? What chance of winning would that give you?

## The History

The Monty Hall Problem is a classic probability puzzle, named for its similarity to the game show “Let’s Make a Deal”, which was hosted by Monty Hall. The problem was made famous when Marilyn vos Savant answered it correctly in her column in a popular magazine, and thousands of readers wrote letters to the magazine arguing her solution was wrong!

The solution can be counter-intuitive, so give it some thought and then scroll down to see the Monty Hall Problem explained.

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## 7 Matchstick Equation Puzzles

In matchstick puzzles, you are presented with an incorrect equation made using matchsticks, and you must move 1 or more matchsticks to turn it into a valid equation.

You must use all of the matches, and you are not allowed to make an inequality symbol such as ≠, ≥, >, <, or ≤.

Try these 7 fun matchstick equation puzzles!

7 + 2 = 9

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## Color of the Last Ball

There is a bag with 20 blue balls and 13 red balls. Randomly remove 2 balls from the bag:

• If they are the same color, replace them with a blue ball
• If they are different colors, replace them with a red ball

Repeat this process until there is just 1 ball remaining. What is the color of the last ball?

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## 10 Clever Riddles with Answers

Do some creative thinking and try to solve these 10 clever riddles:

#### Riddle #1

What do you usually have to break before you can use it?

An egg

#### Riddle #2

What do you need to answer even though it never asks a question?

The telephone

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## Matchstick Equation 4

Move exactly 2 matches to make this a valid equation.

Bonus: find two different solutions.

In matchstick equation puzzles, you are not allowed to make an inequality symbol such as ≠, ≥, >, <, or ≤. That would make it too easy!

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## 8 Easy Rebus Puzzles for Kids

A rebus is puzzle in which words, objects, or symbols are arranged in a way to indirectly represent a commonly known word or phrase. Solving rebus puzzles can be a fun and easy way for kids to think both creatively and analytically.

Here are 8 easy rebus puzzles for kids to get started:

## Rebus 1

HANDED

#### Click for Solution to Rebus 1

Red handed
(“Handed” is written in red text)

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## Mate in 2 Chess Puzzle 3

White to play and mate in 2.

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## Maximize Triangle Area

If a triangle has two sides with lengths 3 and 4, what should the length of the third side be in order to maximize the area of the triangle?

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## Compound Word Puzzle 3

Compound words are words that are composed of two or more other words, like high + light = highlight.

Can you make compound words out of the following three words by adding the same 4-letter word either before or after each word?

• CROSS
• WORKS
• WILD
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## Multiple of 24

Prove that for all prime numbers p > 3, (p2 – 1) is a multiple of 24.

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## Most Frequent Digit

What is the most frequent digit among the numbers between 1 and 1000 (inclusive)? Consider only base-10 whole numbers.

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## Same Birthday in Line

There is a long line of people waiting to see a new movie. They announce that the first person to have the same birthday as someone standing before them in the line gets to meet one of the actors in the movie.

What place in line would maximize your chances of winning? Assume birthdays are uniformly distributed through the year.

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## Prison Keys Strategy

A prison warden was feeling capricious and played a game with the prison keys:

1. Each prisoner is handed a key to another prisoner’s cell.
2. Each prisoner will know which other prisoner was initially given the key to their cell (but does not know whose key they were handed).
3. Each day, when all prisoners are out of their cells and no one is watching, each prisoner is allowed to place keys in another prisoner’s cell.
4. Each night, each prisoner can collect any keys placed in their cell.
5. The prisoners can summon the warden when they’re sure everyone has their own key – but if they are wrong, they’re immediately executed.
6. The prisoners can discuss a strategy beforehand but cannot communicate in any way after keys are handed out.

What is the fewest number of days it would take for the prisoners to be sure everyone has their key? What was the strategy to achieve this?

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## Digital Sum of the Sum

The digital sum of a number is just the sum of the individual digits. E.g., the digital sum of 123 is 1 + 2 + 3 = 6.

• The digital sum of x is 42
• The digital sum of y is 67
• When x and y are added, you have to “carry the 1” exactly five times (e.g., if you add 8 and 9, you “carry the 1” once to get a “1” in the tens digit, thereby getting 17)

What is the digital sum of z = x + y?

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## Sharing Game Theory Puzzle

In this sharing game theory puzzle, 3 friends take turns taking from a jar of 1000 candies to share. For example, the 1st friend could take 500 candies, then the 2nd friend could take 400, and the 3rd friend would take the remaining 100.

No one wants to be seen as greedy, but no one wants to end up with the fewest candies either. As such, their goals are (in order of preference):

1. Not end up with the most candies, nor the fewest candies
2. End up with as many candies as possible

All of them are logical, rational, know each other’s goals, but cannot communicate before or during sharing. How many candies should each friend end up with?

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## I Am Normally Below You Riddle

I am a 5-letter word. I am normally below you.

If you remove my 1st letter, I am normally above you.

If you remove my 1st and 2nd letters, I am all around you.

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## Rebus Puzzle 18

What common word or phrase is this rebus referring to?

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## Rock Paper Scissors Puzzle

A rock paper scissors puzzle:

• Anya played 10 games of rock paper scissors against Blake
• Each time there was a winner (no ties)
• Anya used rock 2 times, paper 2 times, and scissors 6 times, but you don’t know the order
• Blake used rock 2 times, paper 4 times, and scissors 4 times, but you don’t know the order

How many games did each player win?

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## But Never Moves

What can go through towns and cities, over hills and mountains, but never moves?

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## Zero-less Factors

What two numbers contain no zeroes and can be multiplied together to produce 100000?

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## How Many Friday the 13th in a Year

Some consider Friday the 13th (any Friday that falls on the 13th day of a month) unlucky.

In a calendar year, how many Friday the 13th can occur? Find both the minimum and maximum.

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## Ferry Boat Problem

Two ferry boats serve the same route on a river, but travel at different speeds. They depart from opposite ends of the river at the same time, meeting at a point 720 yards from the nearest shore.

When each boat reaches the other side, it takes 10 minutes to unload and load passengers, then begins the return trip. This time, the boats meet at a point 400 yards from the other shore.

How wide is the river?

The ferry boat problem is created by well-known puzzle author Sam Loyd.

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## Converge to an Integer

Given the iterative formula:

xn+1 = sqrt(xn) + a

There are some values of a for which a positive starting value for x results in this formula converging to an integer.

For example, if a = 2, you would observe that xn+1 = sqrt(xn) + 2 eventually converges to 4 for any positive starting value.

What form must a take in order for this formula to converge to an integer?

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## Sum of Powers

Find a combination of three different positive integers x, y, and z such that:

x3 + y3 = z4

Hint: there’s a better way than brute force / trial & error.

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## Finish My Wordle

These Wordle puzzles are nearly complete, you just need to finish them by figuring out the correct word. In each of these 5 puzzles, there should be just one or two valid answers remaining – find them!

Haven’t played Wordle before? You get 6 tries to guess the 5-letter English word, and for each guess you are shown whether each letter is in the right place in the word (green), in the word but in the wrong place (yellow), or not in the word at all (gray).