# Queen's Tour/Examples

## Examples of Queen's Tours

### $3 \times 3$ Chessboard

As can be seen, the queen's tour on a $3 \times 3$ chessboard can be achieved in $2 \times 3 - 2 = 4$ moves.

However, the queen needs to go outside the $3 \times 3$ chessboard in order to do it.

### $4 \times 4$ Chessboard

As can be seen, the queen's tour on a $4 \times 4$ chessboard can be achieved in $2 \times 4 - 2 = 6$ moves.

However, the queen needs to go outside the $4 \times 4$ chessboard in order to do it.

### $5 \times 5$ Chessboard

As can be seen, the queen's tour on a $5 \times 5$ chessboard can be achieved in $2 \times 5 - 2 = 8$ moves.

Notice how the queen does not need to go outside the $5 \times 5$ chessboard in order to do it.

### $7 \times 7$ Chessboard

As can be seen, a re-entrant queen's tour on a $7 \times 7$ chessboard can be achieved in $2 \times 7 - 2 = 12$ moves.

### $8 \times 8$ Chessboard

Here are three examples of a re-entrant queen's tour on a $8 \times 8$ chessboard, achieved in $2 \times 8 - 2 = 14$ moves.