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 29 筆
第 13 頁
... divided by : a . 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 ...
... divided by : a . 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 ...
第 56 頁
... divided by 7. So it is natural to study these remainders . The first few powers of 2 are 2 , 4 , 8 , 16 , 32 , 64 , . . . , and their remainders when divided by 7 are 2 , 4 , 1 , 2 , 4 , 1 , .... These remainders will keep repeating ...
... divided by 7. So it is natural to study these remainders . The first few powers of 2 are 2 , 4 , 8 , 16 , 32 , 64 , . . . , and their remainders when divided by 7 are 2 , 4 , 1 , 2 , 4 , 1 , .... These remainders will keep repeating ...
第 117 頁
... divided . 53a . Denote by T1 the number of ways in which the given n - gon P can be divided into triangles by diagonals which do not intersect inside P. It is convenient to make the convention that T2 1. We will first derive an ...
... divided . 53a . Denote by T1 the number of ways in which the given n - gon P can be divided into triangles by diagonals which do not intersect inside P. It is convenient to make the convention that T2 1. We will first derive an ...
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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