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 57 筆
第 28 頁
... given no definition applicable to this case . To formulate such a definition , consider the following more general problem . Let there be given an infinite sequence of numbers A1 , A2 , A3 , ... Suppose that the first N of these numbers ...
... given no definition applicable to this case . To formulate such a definition , consider the following more general problem . Let there be given an infinite sequence of numbers A1 , A2 , A3 , ... Suppose that the first N of these numbers ...
第 34 頁
... given direction and interpret the term " at random " as follows ( fig . 11a ) . Draw the diameter which is perpen- dicular to the given direction ; each chord is uniquely determined by specifying the point at which it meets this ...
... given direction and interpret the term " at random " as follows ( fig . 11a ) . Draw the diameter which is perpen- dicular to the given direction ; each chord is uniquely determined by specifying the point at which it meets this ...
第 153 頁
... given in the remark . Let us suppose , however , that instead of being given a blank sheet of paper , A is given a slip already marked with a plus . He can then either leave it alone or change it to a minus , and the probability that he ...
... given in the remark . Let us suppose , however , that instead of being given a blank sheet of paper , A is given a slip already marked with a plus . He can then either leave it alone or change it to a minus , and the probability that he ...
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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 length mathematical induction maximum number multiple 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