Challenging Mathematical Problems with Elementary Solutions, 第 1 卷Holden-Day, 1964 - 440 頁 |
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第 1 到 3 筆結果,共 21 筆
第 84 頁
... controlled . Con- versely , if there is a rook on each of the 4 middle rows and each of the 3 middle columns , then the board is controlled . We now have to distinguish two cases . In case 1 , one rook is placed in the lightly shaded ...
... controlled . Con- versely , if there is a rook on each of the 4 middle rows and each of the 3 middle columns , then the board is controlled . We now have to distinguish two cases . In case 1 , one rook is placed in the lightly shaded ...
第 90 頁
... controlled by another is [ ( n + 1 ) / 2 ] 2 . Remark . By considering fig . 37b , it is not hard to prove that for odd n there is exactly one arrangement of ( n + 1 ) 2 / 4 kings on an n × n board for which none of the kings lies on a ...
... controlled by another is [ ( n + 1 ) / 2 ] 2 . Remark . By considering fig . 37b , it is not hard to prove that for odd n there is exactly one arrangement of ( n + 1 ) 2 / 4 kings on an n × n board for which none of the kings lies on a ...
第 99 頁
... controlled by another . Therefore , the total number of knights which can be arranged in such a way on the chessboard is at most 4 × 8 = 32 . 42b . We must determine how many arrangements of 32 knights on a chessboard are such that none ...
... controlled by another . Therefore , the total number of knights which can be arranged in such a way on the chessboard is at most 4 × 8 = 32 . 42b . We must determine how many arrangements of 32 knights on a chessboard are such that none ...
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A₁ A₂ An+m arrangements b₁ B₂ binomial coefficients binomial theorem bishops black squares C₁ chessboard chord circle coefficient color column compute the number Consequently consider corresponding customers denote determine the number diagonals digits dihedral angle divided divisible draw equally likely possible equation equidistant equivalence classes exactly example experiment favorable outcomes follows formula given Hence inclusion and exclusion intersection k-gons knights L₁ length mathematical induction maximum number n-gon number of different number of favorable number of paths number of shortest obtain pairs partition passengers plane points A1 polygons positive integers possible outcomes Pr{E probability theory problem 54 prove queens rectangle relatively prime remaining required probability rooks segment selected at random sequence shortest paths side solution to problem solved sphere square controlled Suppose T₂ total number triangle unfavorable values vertex vertices