Selecting squares from chessboard

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In summary, the probability of selecting three one by one squares at random from a chessboard and forming the letter 'L' is 49/64C3. This calculation assumes that the orientation of the 'L' does not matter.
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utkarshakash
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Homework Statement


If three one by one squares are selected at random from the chessboard, then the probability that they form the letter 'L' is

Homework Equations



The Attempt at a Solution


Total number of ways to choose 3 squares is 64C3. Starting from the 1st square at upperleft corner of 1st row, there is only one way to choose the remaining two squares from the second row adjacent to it such that they form the letter L and this is possible for all the 7 squares(excluding the 8th one) present in 1st row. Thus, it is 7 squares for one row. Similarly, for every 7 rows present(excluding the 8th one), it sums up to 7*7=49. The probability is 49/64C3. But this is not correct!
 
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  • #2
I think it does not matter how the "L" is oriented. If it appears as "L" from a different side, it counts as well.
 

FAQ: Selecting squares from chessboard

What is the purpose of selecting squares from a chessboard?

The purpose of selecting squares from a chessboard is to determine the specific locations of the chess pieces in a game. This allows players to make strategic moves and plan their next moves accordingly.

How do you select a square from a chessboard?

To select a square from a chessboard, you simply need to identify the row and column of the square in question. This can be done by using the alphanumeric notation system commonly used in chess, where each square is assigned a letter and number (e.g. A1, B2, etc.).

Can squares be selected more than once in a chess game?

Yes, squares can be selected multiple times in a chess game. This can happen when a piece is moved to a different square, or when a player is considering different strategic options and visualizing their potential moves.

Are there any rules or limitations for selecting squares in a chess game?

Yes, there are rules and limitations for selecting squares in a chess game. For example, each player can only select one square at a time, and a piece can only be moved to a square if it follows the specific movement rules for that piece.

What are some common strategies for selecting squares in a chess game?

There are many different strategies for selecting squares in a chess game, as it ultimately depends on the player's style and the current board position. However, some common strategies include controlling the center of the board, protecting important pieces and controlling key squares, and setting up potential checkmate combinations.

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