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 21 筆
第 40 頁
... plane ABC . Thus there is one and only one plane ПI equidistant from A , B , C , D with A , B , C on one side of it and D on the other side . By the same reasoning there is exactly one plane equidistant from A , B , C , D with C ( or B ...
... plane ABC . Thus there is one and only one plane ПI equidistant from A , B , C , D with A , B , C on one side of it and D on the other side . By the same reasoning there is exactly one plane equidistant from A , B , C , D with C ( or B ...
第 103 頁
... plane.2 Suppose that k of the lines have already been drawn in the plane ; let us draw the ( k + 1 ) st line and see by how much it increases the number of pieces into which the plane is divided . The ( k + 1 ) st line meets each of the ...
... plane.2 Suppose that k of the lines have already been drawn in the plane ; let us draw the ( k + 1 ) st line and see by how much it increases the number of pieces into which the plane is divided . The ( k + 1 ) st line meets each of the ...
第 104 頁
... plane into two parts , the total number of parts after drawing the n - th circle is 2 + 2 + 4 + 6 + 8 + + 2 ( n − 1 ) = 2 + 2 ( 1 + 2 + 3 + ··· + ( n − 1 ) ) = 2 + 25 n ( n 2 - 1 ) = n2 − n + 2 . 45a . n planes will divide 3 ...
... plane into two parts , the total number of parts after drawing the n - th circle is 2 + 2 + 4 + 6 + 8 + + 2 ( n − 1 ) = 2 + 2 ( 1 + 2 + 3 + ··· + ( n − 1 ) ) = 2 + 25 n ( n 2 - 1 ) = n2 − n + 2 . 45a . n planes will divide 3 ...
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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 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 total number triangle unfavorable values vertex vertices