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 13 頁
... diagonals of a convex n - gon meet if no three diagonals intersect inside the n - gon ? 47. * Into how many parts do the diagonals of a convex n - gon divide the interior of the n - gon if no three diagonals intersect ? 48. Two ...
... diagonals of a convex n - gon meet if no three diagonals intersect inside the n - gon ? 47. * Into how many parts do the diagonals of a convex n - gon divide the interior of the n - gon if no three diagonals intersect ? 48. Two ...
第 108 頁
... diagonal joining the second and fourth points , and no other pair of diagonals joining these four points will intersect within the n - gon ( see fig . 50 ) . By associating to each set of four vertices the point at which two of its ...
... diagonal joining the second and fourth points , and no other pair of diagonals joining these four points will intersect within the n - gon ( see fig . 50 ) . By associating to each set of four vertices the point at which two of its ...
第 114 頁
... diagonals intersect ( fig . 54b ) . The sides AB and A , B of this triangle are parts of diagonals А1 , and AA of the n - gon ; our triangle is one of the four triangles into which the quadrilateral А12 , is divided by its diagonals ...
... diagonals intersect ( fig . 54b ) . The sides AB and A , B of this triangle are parts of diagonals А1 , and AA of the n - gon ; our triangle is one of the four triangles into which the quadrilateral А12 , is divided by its diagonals ...
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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