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 15 筆
第 108 頁
... joining the first and third points will intersect the diagonal joining the second and fourth points , and no other pair of diagonals joining these four points will intersect within the n - gon ( see fig . 50 ) . By associating to each ...
... joining the first and third points will intersect the diagonal joining the second and fourth points , and no other pair of diagonals joining these four points will intersect within the n - gon ( see fig . 50 ) . By associating to each ...
第 137 頁
... joining the intersection ( 1,0 ) to the intersection ( n - m + 1 , m ) , that is , ( 1 ) . m The second class shall consist of those paths which start by going one block up the " vertical " street to the intersection ( 0,1 ) and then ...
... joining the intersection ( 1,0 ) to the intersection ( n - m + 1 , m ) , that is , ( 1 ) . m The second class shall consist of those paths which start by going one block up the " vertical " street to the intersection ( 0,1 ) and then ...
第 170 頁
... joining A , to An + m and having a vertex on the line L1 coincides with the number of paths joining Ao ' to An + m . But these latter paths each consist of n + 1 horizontal ― segments and m - 1 vertical segments ; there are hence of ...
... joining A , to An + m and having a vertex on the line L1 coincides with the number of paths joining Ao ' to An + m . But these latter paths each consist of n + 1 horizontal ― segments and m - 1 vertical segments ; there are hence of ...
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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