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How many squares does a queen attack?

chessboardcountingqueens

A queen stands alone on an 8 by 8 chessboard.

  1. How many squares does she attack from one of the four central squares (d4, e4, d5, e5)?
  2. How many from a corner?
  3. Which squares give the fewest, and why does the total differ by position?
Show a hint

Count the row, the column and the two diagonals separately, not including the queen's own square.

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Balls and Bins and the Birthday ProblemBinomial Coefficients and Pascal's TriangleBurnside's Lemma and Polya CountingCatalan NumbersCounting: Permutations and Combinations

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