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 12 筆
第 80 頁
... placed on the k - th column from the left as shown in fig . 31b for n = 10 . In the case of odd n the situation is somewhat different in that the number of white squares differs from the number of black squares . However , even in this ...
... placed on the k - th column from the left as shown in fig . 31b for n = 10 . In the case of odd n the situation is somewhat different in that the number of white squares differs from the number of black squares . However , even in this ...
第 84 頁
... placed on this board so as to control it ? Suppose that one of the 4 middle rows did not contain a rook . Then all of its squares would have to be controlled vertically ; but since there are at least 5 such squares , this is impossible ...
... placed on this board so as to control it ? Suppose that one of the 4 middle rows did not contain a rook . Then all of its squares would have to be controlled vertically ; but since there are at least 5 such squares , this is impossible ...
第 87 頁
... placed it eliminates the row it is on from further use , thus leaving only 4 rows available for the rooks in B. Of these rooks , 2 must be on the same column , and 1 on each of the other 2 columns . There are 3 ways of picking the ...
... placed it eliminates the row it is on from further use , thus leaving only 4 rows available for the rooks in B. Of these rooks , 2 must be on the same column , and 1 on each of the other 2 columns . There are 3 ways of picking the ...
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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