Logic
# Chess

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?

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?

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?