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 32 筆
第 66 頁
... gives the answer to the problem because any other representation can be reduced to one of this type by reordering its terms ( which is allowed by the conditions of the problem ) . = We now introduce the quantities a , b , c defined by a ...
... gives the answer to the problem because any other representation can be reduced to one of this type by reordering its terms ( which is allowed by the conditions of the problem ) . = We now introduce the quantities a , b , c defined by a ...
第 181 頁
... gives the total number of paths from A to An + m which pass through D , and the second gives the number of such paths which also pass through D1 ) . The number of such paths from Ao ' to An + m is Since NAD2 NA'D2N D1An + - NA'D1N ...
... gives the total number of paths from A to An + m which pass through D , and the second gives the number of such paths which also pass through D1 ) . The number of such paths from Ao ' to An + m is Since NAD2 NA'D2N D1An + - NA'D1N ...
第 197 頁
... gives a remainder of 8 upon division by 16 and a remainder of 5 upon division by 9 , then n has to have the form 144m + 104 : of the numbers of the form 144m + t , where t = 8 , 24 , 40 , 56 , 72 , 88 , 104 , 120 , 136 , only the ...
... gives a remainder of 8 upon division by 16 and a remainder of 5 upon division by 9 , then n has to have the form 144m + 104 : of the numbers of the form 144m + t , where t = 8 , 24 , 40 , 56 , 72 , 88 , 104 , 120 , 136 , only the ...
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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