Challenging Mathematical Problems with Elementary Solutions: Combinatorial analysis and probability theoryHolden-Day, 1964 |
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第 1 到 3 筆結果,共 12 筆
第 76 頁
... rooks on the board to control the square on which another lies , it is necessary and sufficient that no two rooks lie in the same row or in the same column . Hence the total number of rooks cannot exceed n ; on the other hand , it is ...
... rooks on the board to control the square on which another lies , it is necessary and sufficient that no two rooks lie in the same row or in the same column . Hence the total number of rooks cannot exceed n ; on the other hand , it is ...
第 77 頁
... rooks to control all squares of an nx n chessboard . In fact , if there were less than n rooks on the board , there would be a column on which there was no rook and a row on which there was no rook ; the square common to this row and ...
... rooks to control all squares of an nx n chessboard . In fact , if there were less than n rooks on the board , there would be a column on which there was no rook and a row on which there was no rook ; the square common to this row and ...
第 87 頁
... rooks are in A , and the other 3 are in B. In case 1 there are 3 ways to pick the column containing 3 rooks . Once it is chosen there are Then there are 2 ! = 5 = 3 10 ways to place the 3 rooks on it . 2 ways to place the other 2 rooks ...
... rooks are in A , and the other 3 are in B. In case 1 there are 3 ways to pick the column containing 3 rooks . Once it is chosen there are Then there are 2 ! = 5 = 3 10 ways to place the 3 rooks on it . 2 ways to place the other 2 rooks ...
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常見字詞
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 G₁ given Hence inclusion and exclusion intersection k-gons knights length mathematical induction maximum number n-gon number of different number of favorable number of paths number of shortest obtain pairs partition passengers plane polygons positive integers possible outcomes Pr{E probability theory problem 54 prove queens rectangle relatively prime remaining required probability rooks S₁ segment selected at random sequence shortest paths side solution to problem solved sphere square controlled Suppose T₂ total number triangle unfavorable values vertex vertices