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 52 筆
第 41 頁
... Consider first case 1 , and suppose for example that A , B , C are on one side of s , while D is on the other side . There is a unique circle or straight line t passing through A , B , C ( fig . 16 ) . Moreover t does not pass through D ...
... Consider first case 1 , and suppose for example that A , B , C are on one side of s , while D is on the other side . There is a unique circle or straight line t passing through A , B , C ( fig . 16 ) . Moreover t does not pass through D ...
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 - th ) ...
... 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 - th ) ...
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 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