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 52 筆
第 22 頁
... consider the case of an experiment with N equally likely outcomes , N of them in F and NEOF of them in EF . Then Pr { E | F } = NEOFN NFN = NEOF NF Thus Pr { E F } is the fraction of the outcomes of F which are also in E. If we select ...
... consider the case of an experiment with N equally likely outcomes , N of them in F and NEOF of them in EF . Then Pr { E | F } = NEOFN NFN = NEOF NF Thus Pr { E F } is the fraction of the outcomes of F which are also in E. If we select ...
第 160 頁
... consider these two cases separately . If the 1st address is written on the 2nd envelope , then in order that the outcome be unfavorable , it is necessary and sufficient that none of the remaining n − 2 envelopes ( the 3rd through n ...
... consider these two cases separately . If the 1st address is written on the 2nd envelope , then in order that the outcome be unfavorable , it is necessary and sufficient that none of the remaining n − 2 envelopes ( the 3rd through n ...
第 224 頁
... consider only the case of even n and to produce for this case an admissible arrangement of the n queens in which the centermost positive diagonal is left empty . ( The case of odd n can then be handled by adding an extra row and column ...
... consider only the case of even n and to produce for this case an admissible arrangement of the n queens in which the centermost positive diagonal is left empty . ( The case of odd n can then be handled by adding an extra row and column ...
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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 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 total number triangle unfavorable values vertex vertices