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 39 筆
第 170 頁
... m . But these latter paths each consist of n + 1 horizontal ― segments and m - 1 vertical segments ; there are hence of them . ( m + m ) Thus in the problem under consideration there are a total of ( n + m ) m ( equally likely ) ...
... m . But these latter paths each consist of n + 1 horizontal ― segments and m - 1 vertical segments ; there are hence of them . ( m + m ) Thus in the problem under consideration there are a total of ( n + m ) m ( equally likely ) ...
第 182 頁
... m is ND34n + m NA'D2 NDзAn + m - NA'D2 ND2D ND1d + m - · · Ν NA'D2 ND2D , NDз4n + m + NA0'D1 · Ñ d1d2 · Nd2d3 · ND3An + m ; and here it is again easy to see that the number of paths from A to An + m is exactly twice the number of paths ...
... m is ND34n + m NA'D2 NDзAn + m - NA'D2 ND2D ND1d + m - · · Ν NA'D2 ND2D , NDз4n + m + NA0'D1 · Ñ d1d2 · Nd2d3 · ND3An + m ; and here it is again easy to see that the number of paths from A to An + m is exactly twice the number of paths ...
第 191 頁
... m ‡ ( k − 2 ) n + 2 there is no way of decomposing a convex m - gon into k - gons with diagonals which do not intersect within the m - gon . This follows , for example , from the fact that if an m - gon is decomposed into n k - gons ...
... m ‡ ( k − 2 ) n + 2 there is no way of decomposing a convex m - gon into k - gons with diagonals which do not intersect within the m - gon . This follows , for example , from the fact that if an m - gon is decomposed into n k - gons ...
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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 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 total number triangle unfavorable values vertex vertices