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 26 筆
第 41 頁
... passing through A , B , C ( fig . 16 ) . Moreover t does not pass through D , by hypothesis . To be equidistant from the four points , s must be concentric with or parallel to t ( according as t is a circle or a straight line ) and must ...
... passing through A , B , C ( fig . 16 ) . Moreover t does not pass through D , by hypothesis . To be equidistant from the four points , s must be concentric with or parallel to t ( according as t is a circle or a straight line ) and must ...
第 139 頁
... pass through the point ( m - k , k ) - ( n + m - k , k ) ( m - k + k - i , i ) ( 0,0 ) ( m - k , O ) ( m , 0 ) Fig . 60 1 ) ( 1 ) is the number of shortest paths from the point ( 0,0 ) to the point ( n + m − k , k ) which pass through ...
... pass through the point ( m - k , k ) - ( n + m - k , k ) ( m - k + k - i , i ) ( 0,0 ) ( m - k , O ) ( m , 0 ) Fig . 60 1 ) ( 1 ) is the number of shortest paths from the point ( 0,0 ) to the point ( n + m − k , k ) which pass through ...
第 181 頁
... pass through the point D1 is equal to NAD1ND14n + m • = 2N 40 ′ D1 · ND1An + m ? and the number of shortest paths from A to An + m which pass through the point D1 is NA'D , ND , Anim Consequently , there are exactly twice ND1An + m as ...
... pass through the point D1 is equal to NAD1ND14n + m • = 2N 40 ′ D1 · ND1An + m ? and the number of shortest paths from A to An + m which pass through the point D1 is NA'D , ND , Anim Consequently , there are exactly twice ND1An + m as ...
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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 given Hence inclusion and exclusion intersection k-gons knights L₁ 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