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 41 筆
第 51 頁
... contain exactly one number with a 1 among its digits ; the second ten - row consists entirely of numbers with 1's among their digits . Consequently , the first hundred - row contains 10 + 9.1 numbers which have 1's among their digits ...
... contain exactly one number with a 1 among its digits ; the second ten - row consists entirely of numbers with 1's among their digits . Consequently , the first hundred - row contains 10 + 9.1 numbers which have 1's among their digits ...
第 80 頁
... contain a k × k board . For odd k the opposite holds , i.e. , the transformed white squares contain a k × k board and the trans- formed black squares contain a ( k + 1 ) × ( k + 1 ) board . A total of n bishops is also sufficient to ...
... contain a k × k board . For odd k the opposite holds , i.e. , the transformed white squares contain a k × k board and the trans- formed black squares contain a ( k + 1 ) × ( k + 1 ) board . A total of n bishops is also sufficient to ...
第 85 頁
... contain 2 rooks and the other 3 rows contain 1 rook each . The row containing 2 rooks can be chosen in 4 ways ; once it is chosen the 2 rooks can be placed on it in = 10 ways . Then there are 3 rows and 3 columns left to be controlled ...
... contain 2 rooks and the other 3 rows contain 1 rook each . The row containing 2 rooks can be chosen in 4 ways ; once it is chosen the 2 rooks can be placed on it in = 10 ways . Then there are 3 rows and 3 columns left to be controlled ...
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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