Challenging Mathematical Problems with Elementary Solutions, 第 1 卷Holden-Day, 1964 - 440 頁 |
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第 1 到 3 筆結果,共 56 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 52 頁
... exactly once , namely in the term # ( A ) . Next consider an element ƒ which is in exactly two of the sets , say A and B. Then ƒ is counted positively in the terms # ( A ) and # ( B ) , and negatively in the − # ( AB ) . Hence it is ...
... exactly once , namely in the term # ( A ) . Next consider an element ƒ which is in exactly two of the sets , say A and B. Then ƒ is counted positively in the terms # ( A ) and # ( B ) , and negatively in the − # ( AB ) . Hence it is ...
第 174 頁
... exactly m are eliminated by virtue of the shadow cast on the segment AA + 1 . Hence there remain nm illuminated points among Ao , A1 , ... , An + m - 1 . An + m − 1 • For example , in fig . 62b , n = 7 , m = 4 , and exactly 743 of the ...
... exactly m are eliminated by virtue of the shadow cast on the segment AA + 1 . Hence there remain nm illuminated points among Ao , A1 , ... , An + m - 1 . An + m − 1 • For example , in fig . 62b , n = 7 , m = 4 , and exactly 743 of the ...
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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 points A1 polygons positive integers possible outcomes Pr{E probability theory problem 54 prove queens rectangle relatively prime remaining required probability rooks segment selected at random sequence shortest paths side solution to problem solved sphere square controlled Suppose total number triangle unfavorable values vertex vertices