## Eight Queens ★★★

This is a commonly known chess problem.

**The question**:
In how many ways can you arrange eight queens on a standard chessboard in such a way that none of them is attacking any other**?**

**The answer**:
Click here!

The puzzles are marked with stars (★) that show the degree of difficulty of the given puzzle.

This is a commonly known chess problem.

**The question**:
In how many ways can you arrange eight queens on a standard chessboard in such a way that none of them is attacking any other**?**

**The answer**:
Click here!

The figure shown below has nineteen circles that have to be filled with the numbers 1 up to (and including) 19. These numbers have to be placed in such a way that all numbers on any horizontal row and any diagonal line add up to the same sum.

Warning: there are many horizontal and diagonal lines, which have a different number of circles (3, 4, or 5), nevertheless all these sums have to be equal!

**The question**:
How should the nineteen numbers be placed in the net**?**

**The answer**:
Click here!

Thanks to Lucas Jones, we can present you the following puzzle:

A man is going to an Antique Car auction. All purchases must be paid for in cash. He goes to the bank and draws out $25,000.

Since the man does not want to be seen carrying that much money, he places it in 15 envelopes numbered 1 through 15,
in such a way that he can pay any amount up to $25,000 without having to open any envelope.
Each envelope contains the *least* number of bills possible of any available US currency (for example, no two tens instead of a twenty).

At the auction, he makes a successful bid of $8322 for a car. He hands the auctioneer envelopes 2, 8, and 14. After opening the envelopes, the auctioneer finds exactly the right amount.

**The question**:
How many ones did the auctioneer find in the envelopes**?**

**The answer**:
Click here!

In an alley, two ladders are placed crosswise (see the figure below). The lengths of these ladders are resp. 2 and 3 meters. They cross one another at one meter above the ground.

**The question**:
What is the width of the alley**?**

**The answer**:
Click here!

Four white pieces (the mice) are placed on one side of a chessboard, and one black piece (the cat) is placed at the opposite side. The game is played by the following rules:

- black wins if it reaches the opposite side;
- white wins if it blocks black in such a way that black cannot make any move anymore;
- only diagonal moves (of length 1) on empty squares are allowed;
- white only moves forward;
- black can move backward
**and**forward; - black may make the first move, then white makes a move, and so on.

**The question**:
Is this game computable (i.e. is it possible to decide beforehand who wins the game,
no matter how hard his opponent tries to avoid this)**?**

**The answer**:
Click here!

A street of length ** L** is randomly filled with cars (one by one), where the length of a car is the unity of

**The question**:
What is the expectation for the number of cars that can be parked until the street is filled**?**

**The answer**:
Click here!