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 23 筆
第 89 頁
... pieces 2 squares wide and 2 squares high . From the fact that none of these pieces can contain more than one king , it follows that the required maximum number of kings is at most k2 . But it is possible to arrange k2 kings on a 2k × 2k ...
... pieces 2 squares wide and 2 squares high . From the fact that none of these pieces can contain more than one king , it follows that the required maximum number of kings is at most k2 . But it is possible to arrange k2 kings on a 2k × 2k ...
第 102 頁
... pieces by the other lines and consequently increases the total number of pieces by 2n + 1 . It follows from this that the total number of pieces is ( n + 1 ) 2 + n ( 2n + 1 ) = 3n2 + 3n + 1 . 44a . It is clear that n lines will divide ...
... pieces by the other lines and consequently increases the total number of pieces by 2n + 1 . It follows from this that the total number of pieces is ( n + 1 ) 2 + n ( 2n + 1 ) = 3n2 + 3n + 1 . 44a . It is clear that n lines will divide ...
第 103 頁
... pieces n mutually non - parallel lines , no three of which are concurrent , divide 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 ...
... pieces n mutually non - parallel lines , no three of which are concurrent , divide 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 ...
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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 L₁ 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 T₂ total number triangle unfavorable values vertex vertices