# A chessboard divided into four quadrants

Consider the following chessboard:

Divide it into four quadrants as shown:

• First quadrant is renamed as the Rook's quadrant.
• Second quadrant is renamed as the Bishop's quadrant.
• Third quadrant is renamed as the Knight's quadrant.
• Fourth quadrant is renamed as the Queen's quadrant.

Your task is to fill out the empty Queen's quadrant by figuring out the logic used to fill other quadrants.

Queen's quadrant might be :

($$3$$,$$\sqrt(18)$$) | ($$5$$,$$3$$) | ($$5$$,$$3$$) | ($$3$$,$$\sqrt(18)$$)

($$5$$,$$3$$) | ($$8$$,$$\sqrt(8)$$) | ($$8$$,$$\sqrt(8)$$) | ($$5$$,$$3$$)

($$5$$,$$3$$) | ($$8$$,$$\sqrt(8)$$) | ($$8$$,$$\sqrt(8)$$) | ($$5$$,$$3$$)

($$3$$,$$\sqrt(18)$$) | ($$5$$,$$3$$) | ($$5$$,$$3$$) | ($$3$$,$$\sqrt(18)$$)

Explanation:

In each square, the first number is

The number of directions available for the quadrant piece (R,B,N,Q) to move and remain in its quadrant.

And the second number is

The distance that piece would travel to play its longest available move within its quadrant.

For example :

A bishop on b8 can move in 2 directions (South-West or South-East) to stay in its quadrant. The longest move it can do (to d6) is $$\sqrt(8)$$ squares long.
That's why ($$2$$,$$\sqrt(8)$$) is written in square b8.

This assumes :

That you move your knight the way we teach it to beginners (two squares one way, then turn 90°, then one square, totalling three squares) and not directly to its destination (its score would then be $$\sqrt(5)$$ and not $$3$$)