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 14 頁
... divided , and find this number . 53a . * In how many different ways can a convex octagon be decomposed into triangles by diagonals which do not intersect within the octagon ? b . *** Euler's problem . In how many ways can a convex n ...
... divided , and find this number . 53a . * In how many different ways can a convex octagon be decomposed into triangles by diagonals which do not intersect within the octagon ? b . *** Euler's problem . In how many ways can a convex n ...
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 ...
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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