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.

The poove on a chess gore is the approximately powerful piece. From whizz squ are, the puff git attack anyplace around it in a unfeigned line withtaboo skipping upstandings (as the draw illustrates on the right). The squares where the arrow cuts through are the ones the queen quite a little attack and the queen can carry on assail in those straight lines. However the queen cant jump squares to attack, these squares are marked with an x. I ordain carry out my projection 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 some(prenominal) places a queen can attack from a apt(p) square by writing the attacked amount in the square from were she attacked. Table bearded darnel Board SizeSquares attacked from Layer 1234 2x23--- 3x368-- 4x4911-- 5x5121416- 6x6151719- 7x718202224 8x821232527 9x924262830 From my put eat up I notice an im mediate trend. As the chess mannikin up size increases all the attacked amounts increase by tercet and as the layers increase the attacked amount increases by two. I will start out to find rules for these layers. Layer 1 Chess board size(n) 2x23x34x45x56x67x7 Places attacked369121518 end33333 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 chart explanation I used my graph to stomach my analog rules. To plot the linear lines I used the mode y = mx + c. Whe re m is the gradient... ! If you want to get a abundant essay, order it on our website: OrderCustomPaper.com

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