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 30 筆
第 11 頁
... chessboard in such a way that none of them controls the square on which another lies ? In how many different ways can this be done ? b . What is the smallest number of rooks which can be arranged on an nx n chessboard in such a way that ...
... chessboard in such a way that none of them controls the square on which another lies ? In how many different ways can this be done ? b . What is the smallest number of rooks which can be arranged on an nx n chessboard in such a way that ...
第 12 頁
... chessboard ? b . On an n x n chessboard ? 41. What is the greatest number of queens which can be arranged in such a way that no queen lies on a square controlled by another : a . On an 8 x 8 chessboard ? b . *** On an n x n chessboard ...
... chessboard ? b . On an n x n chessboard ? 41. What is the greatest number of queens which can be arranged in such a way that no queen lies on a square controlled by another : a . On an 8 x 8 chessboard ? b . *** On an n x n chessboard ...
第 92 頁
... chess- board ; hence it is impossible to arrange more than eight queens on an 8 × 8 chessboard in such a way that none of them lies on a square controlled by another . Fig . 39 On the other hand , we can actually put 8 queens on the ...
... chess- board ; hence it is impossible to arrange more than eight queens on an 8 × 8 chessboard in such a way that none of them lies on a square controlled by another . Fig . 39 On the other hand , we can actually put 8 queens on the ...
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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 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