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 51 頁
... exactly one number among whose digits a 1 occurs , namely the number 1. In the first hundred - row , each ten - row except the second ( which consists of the numbers from 10 to 19 ) will contain exactly one number with a 1 among its ...
... exactly one number among whose digits a 1 occurs , namely the number 1. In the first hundred - row , each ten - row except the second ( which consists of the numbers from 10 to 19 ) will contain exactly one number with a 1 among its ...
第 174 頁
... exactly m are eliminated by virtue of the shadow cast on the segment A¡A1 + 1 . Hence there remain nm illuminated points among Ao , A1 , ... , An + m − 1 · For example , in fig . 62b , n = 7 , m = 4 , and exactly 7 4 3 of the points ...
... exactly m are eliminated by virtue of the shadow cast on the segment A¡A1 + 1 . Hence there remain nm illuminated points among Ao , A1 , ... , An + m − 1 · For example , in fig . 62b , n = 7 , m = 4 , and exactly 7 4 3 of the points ...
第 195 頁
... exactly 20 integers from 1 to 6Q are relatively prime to 6 , and of the next R integers , at most two can be relatively prime to 6 ( since R is at most 5 ) . Thus a total of 20 + r integers from 1 to N are relatively prime to 6 , where ...
... exactly 20 integers from 1 to 6Q are relatively prime to 6 , and of the next R integers , at most two can be relatively prime to 6 ( since R is at most 5 ) . Thus a total of 20 + r integers from 1 to N are relatively prime to 6 , where ...
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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