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 32 筆
第 107 頁
... intersection four times ( each of these points is the intersection of exactly two diagonals , each of which has two vertices as end - points ) . Thus the number of points of intersection is ( n - 1 ) ( n - 2 ) ( n − 3 ) 6 - - - n ( n ...
... intersection four times ( each of these points is the intersection of exactly two diagonals , each of which has two vertices as end - points ) . Thus the number of points of intersection is ( n - 1 ) ( n - 2 ) ( n − 3 ) 6 - - - n ( n ...
第 108 頁
... intersection and the sets of four vertices . It follows from this that the number of points of intersection equals the number of ways one can choose four vertices from among the n vertices of the n - gon , that is , the number of ...
... intersection and the sets of four vertices . It follows from this that the number of points of intersection equals the number of ways one can choose four vertices from among the n vertices of the n - gon , that is , the number of ...
第 137 頁
... intersection ( 1,0 ) to the intersection ( n m + 1 , m ) , that is , ( m ) . ― The second class shall consist of those paths which start by going one block up the " vertical " street to the intersection ( 0,1 ) and then turn right ; the ...
... intersection ( 1,0 ) to the intersection ( n m + 1 , m ) , that is , ( m ) . ― The second class shall consist of those paths which start by going one block up the " vertical " street to the intersection ( 0,1 ) and then turn right ; 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 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