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 6 頁
... Prove that if A and B are finite sets , then ―― – # ( AUB ) = # ( A ) + # ( B ) − # ( A & B ) . b . Prove that if A , B , and C are finite sets , then # ( A U BU C ) = # ( A ) + # ( B ) + # ( C ) − # ( A ~ B ) - # ( AC ) - # ( B ( C ) ...
... Prove that if A and B are finite sets , then ―― – # ( AUB ) = # ( A ) + # ( B ) − # ( A & B ) . b . Prove that if A , B , and C are finite sets , then # ( A U BU C ) = # ( A ) + # ( B ) + # ( C ) − # ( A ~ B ) - # ( AC ) - # ( B ( C ) ...
第 9 頁
... Prove that if n > m ( m + 1 ) / 2 , the number of partitions of n into m distinct parts is equal to the number of partitions of n- m ( m + 1 ) / 2 into at most m ( not necessarily distinct ) parts . 33a . * Prove that the number of ...
... Prove that if n > m ( m + 1 ) / 2 , the number of partitions of n into m distinct parts is equal to the number of partitions of n- m ( m + 1 ) / 2 into at most m ( not necessarily distinct ) parts . 33a . * Prove that the number of ...
第 230 頁
... prove 1 85a . m + n = Gn - 1 ( compare b . Show that the desired probability P is independent of k . From this it follows that P 86. 1/3 ; 5/9 . = 1 m + n 87a . 1/5 ; 1/100 . b . 1/5 ; 2/5 . 88. 1/7 ; 91/144 . 89. 1/4 ; 1/20 . 90. log 2 ...
... prove 1 85a . m + n = Gn - 1 ( compare b . Show that the desired probability P is independent of k . From this it follows that P 86. 1/3 ; 5/9 . = 1 m + n 87a . 1/5 ; 1/100 . b . 1/5 ; 2/5 . 88. 1/7 ; 91/144 . 89. 1/4 ; 1/20 . 90. log 2 ...
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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 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 T₂ total number triangle unfavorable values vertex vertices