Challenging Mathematical Problems with Elementary Solutions: Combinatorial analysis and probability theoryHolden-Day, 1964 |
搜尋書籍內容
第 1 到 3 筆結果,共 36 筆
第 32 頁
... note first that if 0 ≤ x ≤ y ≤ L , then - p ( y ) = p ( x ) + p ( y − x ) ≥ p ( x ) , since p ( y — x ) ≥ 0 by property ( 1 ) . Thus the function p ( x ) is monotone non - decreasing . Now if x / L is irrational , and n is any ...
... note first that if 0 ≤ x ≤ y ≤ L , then - p ( y ) = p ( x ) + p ( y − x ) ≥ p ( x ) , since p ( y — x ) ≥ 0 by property ( 1 ) . Thus the function p ( x ) is monotone non - decreasing . Now if x / L is irrational , and n is any ...
第 59 頁
... ( Note that the divisor 1 is gotten by taking a b = C = 0. ) Thus there are 5 possibilities for a ( namely 0 , 1 , 2 , 3 , or 4 ) , 3 possibilities for b , and 4 possibilities for c . Since these can be combined in all possible ways , the ...
... ( Note that the divisor 1 is gotten by taking a b = C = 0. ) Thus there are 5 possibilities for a ( namely 0 , 1 , 2 , 3 , or 4 ) , 3 possibilities for b , and 4 possibilities for c . Since these can be combined in all possible ways , the ...
第 198 頁
... Note that there cannot be two different powers of 2 which have the same number of digits and which both begin with a 1. If two distinct powers of 2 are given , the larger must be at least twice the smaller ; hence if both have the same ...
... Note that there cannot be two different powers of 2 which have the same number of digits and which both begin with a 1. If two distinct powers of 2 are given , the larger must be at least twice the smaller ; hence if both have the same ...
其他版本 - 查看全部
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