White to play and mate in 2

Continue reading “Mate in 2 Chess Puzzle 4”# Difficulty – Medium

Medium difficulty brain teasers and puzzles

## Area of the Rectangle

The shaded rectangle is tangent to the circle at the two points indicated, and its bottom right corner lies on the circumference of that circle. What is the area of the rectangle?

Continue reading “Area of the Rectangle”## The Monty Hall Problem Explained

## 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.

Continue reading “The Monty Hall Problem Explained”## 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 ≤.

In each of these 7 fun matchstick equation puzzles, move exactly 1 match to fix the equation:

#### Click for Solution to 1 + 2 = 8

7 + 2 = 9

## 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?

View Solution## Multiple of 24

Prove that for all prime numbers p > 3, (p^{2} – 1) is a multiple of 24.

## 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.

Continue reading “Same Birthday in Line”## 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*?

## 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.

View Solution## 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.

Continue reading “How Many Friday the 13th in a Year”