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 33 筆
第 103 頁
... drawn in the plane ; let us draw the ( k + 1 ) st line and see by how much it increases the number of pieces into which the plane is divided . The ( k + 1 ) st line meets each of the k lines which have already been drawn ; the k points ...
... drawn in the plane ; let us draw the ( k + 1 ) st line and see by how much it increases the number of pieces into which the plane is divided . The ( k + 1 ) st line meets each of the k lines which have already been drawn ; the k points ...
第 142 頁
... drawn ) ; corresponding to each of these outcomes there are four possible outcomes to the drawing of the third card ... drawn be ( in the order 142 SOLUTIONS.
... drawn ) ; corresponding to each of these outcomes there are four possible outcomes to the drawing of the third card ... drawn be ( in the order 142 SOLUTIONS.
第 227 頁
... drawn , of exactly one being drawn , of exactly two being drawn , ... , and of exactly k being drawn equals 1 . 73a . ( 2n ― n 22n - k k b . 22. This result can be derived from part a in the same way that problem 72b follows from 72a ...
... drawn , of exactly one being drawn , of exactly two being drawn , ... , and of exactly k being drawn equals 1 . 73a . ( 2n ― n 22n - k k b . 22. This result can be derived from part a in the same way that problem 72b follows from 72a ...
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A₁ A₂ An+m arrangements b₁ B₂ binomial coefficients binomial theorem bishops black squares 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 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