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 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 , note that 2 * + 3 2x is a multiple of 7 . ― = 8.2x 2x = 7.2x Next we will make a similar analysis of the remainders of x2 when divided by 7. Putting x = 1 , 2 , 3 , 4 , 5 , 6 , 7 we have x2 = 1 , 4 , 9 , 16 , 25 , 36 , 49 ...
... divided by 7 , note that 2 * + 3 2x is a multiple of 7 . ― = 8.2x 2x = 7.2x Next we will make a similar analysis of the remainders of x2 when divided by 7. Putting x = 1 , 2 , 3 , 4 , 5 , 6 , 7 we have x2 = 1 , 4 , 9 , 16 , 25 , 36 , 49 ...
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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常見字詞
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 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