Chess Abstract: Level 3 Challenges


Define a Galloping Queen as a chess piece whose legal move is that of a Knight, and that of a Queen.

What is the minimum value of integer \(n > 1\) such that you can place \(n\) non-attacking Galloping Queens on an \(n \times n\) chessboard?

Try more questions on Galloping Queens

What is the maximum number of bishops on a \( 8 \times 8 \) chessboard, so that they cannot attack each other?

Above is a \(3\times3\) board with 4 knights two white knights and two black knights. As in a standard game of chess, the knight can move only two steps in the horizontal or vertical direction and then one step in the other direction for one move. Define an action as moving a knight of any color.

The objective of the game is to interchange the position of both the black and white knights while alternately moving a knight of different color. The final state of the board is:

Using only actions, what is the minimum number of actions required to complete the game?

What is the maximum number of counters you can place on an \(8 \times 8\) chessboard given that each row, column, ‚Äčand the two main diagonals contain 5 or fewer counters?

A white pawn had been accidentally knocked off the board. Neither player could remember for sure on which square it stood. If neither king has yet moved, where is the pawn?

This problem was inspired by the book Chess Mysteries of Sherlock Holmes by Raymond Smullyan.
This problem is the first one of the set Retrograde Chess.

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