Challenging Mathematical Problems with Elementary Solutions: Combinatorial analysis and probability theoryHolden-Day, 1964 |
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第 1 到 3 筆結果,共 14 筆
第 13 頁
... n straight lines ? b . n circles ? 45 . ** What is the greatest number of parts into which three - dimensional space can be divided by : a . n planes ? b . n spheres ? 46. * In how many points do the diagonals of a convex n - gon meet ...
... n straight lines ? b . n circles ? 45 . ** What is the greatest number of parts into which three - dimensional space can be divided by : a . n planes ? b . n spheres ? 46. * In how many points do the diagonals of a convex n - gon meet ...
第 108 頁
... n - gon ( see fig . 50 ) . By associating to each set of four vertices the point at which two of its diagonals meet , we set up a one - to - one correspondence between the points of intersection and the sets of four vertices . It ...
... n - gon ( see fig . 50 ) . By associating to each set of four vertices the point at which two of its diagonals meet , we set up a one - to - one correspondence between the points of intersection and the sets of four vertices . It ...
第 110 頁
... 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 finally by rm the number of m - gons , where m ...
... 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 finally by rm the number of m - gons , where m ...
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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 length mathematical induction maximum number multiple n-gon number of different number of favorable number of paths number of shortest obtain pairs partition passengers plane polygons positive integers possible outcomes Pr{E probability theory problem 54 prove queens rectangle relatively prime remaining required probability rooks S₁ segment selected at random sequence shortest paths side solution to problem solved sphere square controlled Suppose T₂ total number triangle unfavorable values vertex vertices