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 57 筆
第 39 頁
... 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 the other side of 1 . Suppose for example that A and B are on one side of 1 ...
... 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 the other side of 1 . Suppose for example that A and B are on one side of 1 ...
第 41 頁
... side and B , C on the other . Thus there are a total of three planes in case 2 . Combining the two cases gives a ... side of s . ( By the two sides of a circle we mean , of course , the inside and the outside . ) For they would then lie ...
... side and B , C on the other . Thus there are a total of three planes in case 2 . Combining the two cases gives a ... side of s . ( By the two sides of a circle we mean , of course , the inside and the outside . ) For they would then lie ...
第 43 頁
... 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 concentric with Σ or on a plane parallel to Σ , according as Σ is a sphere or a plane . Con- sequently there ...
... 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 concentric with Σ or on a plane parallel to Σ , according as Σ is a sphere or a plane . Con- sequently there ...
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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