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 31 筆
第 50 頁
... means that among the integers from 0,000,000,000 to 9,999,999,999 there are 910 different numbers which have no 1's ... mean a set of ten integers which consists of some multiple of ten and the next nine integers after it ( for example ...
... means that among the integers from 0,000,000,000 to 9,999,999,999 there are 910 different numbers which have no 1's ... mean a set of ten integers which consists of some multiple of ten and the next nine integers after it ( for example ...
第 197 頁
... means that n ( n - - 2 ) ( n − 4 ) ( n − 6 ) is - ( it is easy to see that in this case it is even - — Thus , n ( n - 1 ) ( n − 2 ) ( n − 3 ) ( n − 4 ) ( n − 5 ) ( n - 6 ) is divisible by 64 if and only if n has the form 41 + 1 or ...
... means that n ( n - - 2 ) ( n − 4 ) ( n − 6 ) is - ( it is easy to see that in this case it is even - — Thus , n ( n - 1 ) ( n − 2 ) ( n − 3 ) ( n − 4 ) ( n − 5 ) ( n - 6 ) is divisible by 64 if and only if n has the form 41 + 1 or ...
第 215 頁
... means that all solutions of ( 1 ) in nonnegative integers are to be considered as equally likely . This is not quite the same as saying that the break points are chosen independ- ently and uniformly from A1 , ... , An - 1 . ) The fact ...
... means that all solutions of ( 1 ) in nonnegative integers are to be considered as equally likely . This is not quite the same as saying that the break points are chosen independ- ently and uniformly from A1 , ... , An - 1 . ) The fact ...
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A₁ A₂ An+m arrangements b₁ b₂ binomial coefficients binomial theorem bishops black squares 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 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 P₁ 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