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 108 頁
... 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 combinations of n elements 4 at a time ...
... 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 combinations of n elements 4 at a time ...
第 113 頁
... vertices of the triangles in question must be either vertices of the n - gon or intersection points of its diagonals . Let us consider separately the following four cases : 1. All three vertices of the triangle are vertices of the n ...
... vertices of the triangles in question must be either vertices of the n - gon or intersection points of its diagonals . Let us consider separately the following four cases : 1. All three vertices of the triangle are vertices of the n ...
第 194 頁
... vertices A and Ap + m + n ' and as shown above , will contain no other vertices of P ' . The path P , corresponds to an outcome in So , since there are no vertices below A „ Ap + m + n • Let / continue moving to the left until it ...
... vertices A and Ap + m + n ' and as shown above , will contain no other vertices of P ' . The path P , corresponds to an outcome in So , since there are no vertices below A „ Ap + m + n • Let / continue moving to the left until it ...
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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