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 60 筆
第 67 頁
... determine the number of pairs of integers ( x , y ) with 0 < x ≤ n / 2 , 0 ≤ y ≤ n / 2 , n / 2 ≤ x + y ≤n . These conditions can be interpreted geometrically as follows . We draw a rectangular coordinate system in the plane as in ...
... determine the number of pairs of integers ( x , y ) with 0 < x ≤ n / 2 , 0 ≤ y ≤ n / 2 , n / 2 ≤ x + y ≤n . These conditions can be interpreted geometrically as follows . We draw a rectangular coordinate system in the plane as in ...
第 166 頁
... determine the numbers a1 , a2 , a10 . ( 10 ) 910- The number a1 of arrangements in which a given capital letter and the corresponding small letter ( say , A and a ) are next to each other can be determined in the following way . Arrange ...
... determine the numbers a1 , a2 , a10 . ( 10 ) 910- The number a1 of arrangements in which a given capital letter and the corresponding small letter ( say , A and a ) are next to each other can be determined in the following way . Arrange ...
第 172 頁
... determine q ( n , m ) , we will then be able to find p ( n , m ) by using this formula . So we will now show how to determine q ( n , m ) . - It is clear that for n ≤ m , q ( n , m ) = 0. Suppose now that n > m and consider any ...
... determine q ( n , m ) , we will then be able to find p ( n , m ) by using this formula . So we will now show how to determine q ( n , m ) . - It is clear that for n ≤ m , q ( n , m ) = 0. Suppose now that n > m and consider any ...
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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