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 48 筆
第 25 頁
... suppose that the probability that he hits it at this distance is 1/2 ( that is , from a distance of 100 yards the hunter hits a running fox just as often as he misses ) . If he misses , the hunter reloads his rifle and shoots again ...
... suppose that the probability that he hits it at this distance is 1/2 ( that is , from a distance of 100 yards the hunter hits a running fox just as often as he misses ) . If he misses , the hunter reloads his rifle and shoots again ...
第 39 頁
... suppose I is a line equidistant from them . If A , B , C were all on the same side of 1 , they would lie on a line parallel to 1 , contradicting the hypothesis . Therefore two of the points are on one side of 7 and the third point is on ...
... suppose I is a line equidistant from them . If A , B , C were all on the same side of 1 , they would lie on a line parallel to 1 , contradicting the hypothesis . Therefore two of the points are on one side of 7 and the third point is on ...
第 43 頁
... suppose Σ is a sphere or plane equidistant from them . Then A , B , C , D , E cannot all be on the same side of Σ . ( By the two sides of a sphere we mean the inside and the outside . ) For if they were , they would lie on a sphere ...
... suppose Σ is a sphere or plane equidistant from them . Then A , B , C , D , E cannot all be on the same side of Σ . ( By the two sides of a sphere we mean the inside and the outside . ) For if they were , they would lie on a sphere ...
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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 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