# To find rules for the number of squares a queen can attack from a point on a chess board and the minimum and maximum squares a queen can attack from a given rectangular chessboard.

Essay by roonyA+, January 2004

The queen on a chess board is the most

powerful piece. From one square, the queen can

attack anywhere around it in a straight line

without skipping squares (as the diagram

illustrates on the right). The squares where the

arrow cuts through are the ones the queen can

attack and the queen can carry on attacking in

those straight lines. However the queen can't jump squares to attack,

these squares are marked with an x.

I will carry out my task systematically, drawing chess grids smallest to largest.

*2 by 2*4 by 4*6 by 6*8 by 8

*3 by 3*5 by 5*7 by 7*9 by 9

I will display how many places a queen can attack from a given square by writing the attacked amount in the square from were she attacked.

Table

Chess Board SizeSquares attacked from Layer

1234

2x23---

3x368--

4x4911--

5x5121416-

6x6151719-

7x718202224

8x821232527

9x924262830

From my table I notice an immediate trend.

As the chess board size increases all the attacked amounts increase by three and as the layers increase the attacked amount increases by two. I will attempt to find rules for these layers.

Layer 1

Chess board size(n)

2x23x34x45x56x67x7

Places attacked369121518

Difference33333

3n=3 x chess board size

6912151821

Places attacked - 3n-3-3-3-3-3-3

3n - 3

369121518

Layer 2

Chess board size(n)3x3

4x45x56x67x78x8

Places attacked81114172023

Difference

33333

3n91215182124

Places attacked - 3n

-1-1-1-1-1-1

3n - 1

81114172023

Layer 3

Chess board size(n)5x5

6x67x78x89x9

Places attacked1619222528

Difference3333

3n

1518212427

Places attacked - 3n11111

3n + 1

1619222528

Layer 4

Chess board size(n)7x7

8x89x9

Places attacked242730

Difference33

3n

212427

Places attacked - 3n333

3n + 3

242730

Graph explanation

I used my graph to support my linear rules. To plot the linear lines I used the method y = mx + c. Where m is the gradient...