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 35 筆
第 66 頁
... corresponding to each representation n = x + y + z we have associated a partition of n into a sum of 1's , 2's , and 3's . For example , to the representation 10 = 5 + 3 + 2 would correspond the partition 101 + 1 + 2 + 3 + 3 , since a 2 ...
... corresponding to each representation n = x + y + z we have associated a partition of n into a sum of 1's , 2's , and 3's . For example , to the representation 10 = 5 + 3 + 2 would correspond the partition 101 + 1 + 2 + 3 + 3 , since a 2 ...
第 173 頁
... corresponding to staircases in which light falls on the base A。( that is , A , does not lie in the shadow thrown by ... correspond to the paths which consist of n + m consecutive unit segments and start respectively at the points Ao ...
... corresponding to staircases in which light falls on the base A。( that is , A , does not lie in the shadow thrown by ... correspond to the paths which consist of n + m consecutive unit segments and start respectively at the points Ao ...
第 193 頁
... corresponding path P will then satisfy . Let A1 + ; = ( i , j ) be any point of P. Then the amount of money in the bank at the ( i + j ) ' th stage of the game is -ai + bj , since i people have withdrawn a dollars each , and j people ...
... corresponding path P will then satisfy . Let A1 + ; = ( i , j ) be any point of P. Then the amount of money in the bank at the ( i + j ) ' th stage of the game is -ai + bj , since i people have withdrawn a dollars each , and j people ...
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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