1. ## CHessboard 2

More Chess Problems,

1. How Many Knights can be placed on a board so that no other knight is in danger of being taken by another Knight and how ?

2. In relation to the earlier Chess puzzle with the Queens, how many different ways are there to arrange those 8 queens on board so neither is in danger of being taken by the other ?

3.Place 4 Knights and 4 Queens on the board so that neither threaten each other.

4. You have a chess board, and a set of dominoes. The dominoes are of such size that they cover exactly 2 squares of the chess board. Obviously since there are 64 squares on the chess board, you can cover it fully with 32 dominoes.
You cut off two diagonally opposite squares on the chess board so that only 62 squares are left. How many dominoes can you fit on the board such that each dominoe covers exactly 2 squares? Dominoes overlapping each other and dominoes sticking out are not allowed.

5.Place One Knight and 4 Queens on a board so that every square is either occupied or attacked.

6. Finally, Place all 16 white pieces on the board so that the number of possible moves is a maximum.

2. ## Re: CHessboard 2

4. <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>Although there are 62 squares left, you can't fit 31 dominoes on the board, only 30.
Each domino covers a white square and a black square. When you remove two diagonally oppposite squares, you remove two squares of the same color, so you are left with 30 squares of one color and 32 of the other. Thirty dominos will cover 30 white and 30 black squares, but 2 squares of the same color will remain uncovered.</font color=yellow></span hi>

3. ## Re: CHessboard 2

Did you google that Hans ?

4. ## Re: CHessboard 2

No, I didn't Google for it, but I must admit that I had seen (and solved) #4 a long time ago, I forget where. So I didn't have to think long about it now.

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