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 22 筆
第 77 頁
... column or one rook in each row . For otherwise there would be a row and a column , neither of which contained any rooks ; and the square common to this row and column would not be controlled by any of the rooks . Conversely , if there ...
... column or one rook in each row . For otherwise there would be a row and a column , neither of which contained any rooks ; and the square common to this row and column would not be controlled by any of the rooks . Conversely , if there ...
第 87 頁
... columns . Then there are ( 2 ) = 3 ways to put 2 rooks on the other chosen column ( since only 3 of its rows are still usable ) . Finally , the position of the rook on the remaining column is completely determined . Hence we get 3 10 3 ...
... columns . Then there are ( 2 ) = 3 ways to put 2 rooks on the other chosen column ( since only 3 of its rows are still usable ) . Finally , the position of the rook on the remaining column is completely determined . Hence we get 3 10 3 ...
第 95 頁
... column lies in the 5th row , that in the 4th column lies in the 7th row , etc. ) . In the n / 2 - 3 columns starting with the ( n / 2 + 3 ) rd and ending with the ( n 1 ) st , queens are put in every other row , starting with the 6th ...
... column lies in the 5th row , that in the 4th column lies in the 7th row , etc. ) . In the n / 2 - 3 columns starting with the ( n / 2 + 3 ) rd and ending with the ( n 1 ) st , queens are put in every other row , starting with the 6th ...
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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