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 17 筆
第 10 頁
... occupied by another piece . A bishop controls all squares of the diagonals on which it lies up to and including the first square occupied by another piece . The queen controls all squares of the row , column , and diagonals on which it ...
... occupied by another piece . A bishop controls all squares of the diagonals on which it lies up to and including the first square occupied by another piece . The queen controls all squares of the row , column , and diagonals on which it ...
第 86 頁
... occupied by a rook . Suppose that one of the two rows marked by arrows was not occupied . Then its squares would have to be controlled vertically , so that each of the middle 5 columns would have to be occupied . Thus we have proved ...
... occupied by a rook . Suppose that one of the two rows marked by arrows was not occupied . Then its squares would have to be controlled vertically , so that each of the middle 5 columns would have to be occupied . Thus we have proved ...
第 163 頁
... occupied . For a given set of r carriages we know from part a that the p passengers can be put into them so that ... occupied ( we consider the number m to be fixed ) . Now consider f ( p + 1 , r ) . From each of the f ( p , r ) ...
... occupied . For a given set of r carriages we know from part a that the p passengers can be put into them so that ... occupied ( we consider the number m to be fixed ) . Now consider f ( p + 1 , r ) . From each of the f ( p , r ) ...
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常見字詞
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