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 8 筆
第 110 頁
... polygon . Second solution . The diagonals of an n - gon divide it into smaller polygons . We denote by r , the number of triangles among these polygons , by r , the number of quadrilaterals , by r , the number of pentagons , etc. , and ...
... polygon . Second solution . The diagonals of an n - gon divide it into smaller polygons . We denote by r , the number of triangles among these polygons , by r , the number of quadrilaterals , by r , the number of pentagons , etc. , and ...
第 123 頁
... polygons there are with vertices at Ao , A1 , ... , Ap - 1 , counting two polygons as different if they differ either in shape or location . To obtain a polygon we join A , to any point A1 , other than A。, then join A ,, to any point A ...
... polygons there are with vertices at Ao , A1 , ... , Ap - 1 , counting two polygons as different if they differ either in shape or location . To obtain a polygon we join A , to any point A1 , other than A。, then join A ,, to any point A ...
第 124 頁
... polygon each vertex As is joined to As + t , where t is a fixed number satisfying 1 ≤ t≤ p − 1. But as in our discussion of the method for obtaining all polygons , each regular polygon will arise twice in this process , since t and p ...
... polygon each vertex As is joined to As + t , where t is a fixed number satisfying 1 ≤ t≤ p − 1. But as in our discussion of the method for obtaining all polygons , each regular polygon will arise twice in this process , since t and p ...
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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